Els costats mesuren: a=#a, b = #b, d = #d i f = #f
 |
Calcula:
a) la proporció (raó de semblança) entre el triangle gran i el petit.
b) c
c) e
]]>
Teorema de Pitàgores
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«msqrt mathcolor=¨#003300¨»«msup»«mi mathvariant=¨bold¨»b«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»+«/mo»«msup»«mi mathvariant=¨bold¨»c«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«/msqrt»«/math»
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»b«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«msqrt mathcolor=¨#003300¨»«msup»«mi mathvariant=¨bold¨»a«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»-«/mo»«msup»«mi mathvariant=¨bold¨»c«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«/msqrt»«/math»
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»c«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«msqrt mathcolor=¨#003300¨»«msup»«mi mathvariant=¨bold¨»a«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»-«/mo»«msup»«mi mathvariant=¨bold¨»b«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«/msqrt»«/math»
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»a«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»=«/mo»«msqrt mathcolor=¨#007F00¨»«msup»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«/mrow»«/mfenced»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»+«/mo»«msup»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»c«/mi»«/mrow»«/mfenced»«mn mathvariant=¨bold¨»2«/mn»«/msup»«/msqrt»«/mrow»«/mstyle»«/math»
Recorda de posar TOT el radicand entre parèntesis a la calculadora... I SIMPLIFICA
]]>«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»b«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»=«/mo»«msqrt mathcolor=¨#000066¨»«msup»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«/mfenced»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»-«/mo»«msup»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»c«/mi»«/mrow»«/mfenced»«mn mathvariant=¨bold¨»2«/mn»«/msup»«/msqrt»«/mstyle»«/math»
i simplifiquem el resultat.
]]>«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»c«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»=«/mo»«msqrt mathcolor=¨#000066¨»«msup»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«/mfenced»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»-«/mo»«msup»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«/mrow»«/mfenced»«mn mathvariant=¨bold¨»2«/mn»«/msup»«/msqrt»«/mstyle»«/math»
i simplifiquem el resultat.
]]>|
Raons trigonomètriques |
|
|
|
sin B = b/a (oposat/hipotenusa) cos B = c/a (adjacent/hipotenusa) tg B = b/c (oposat/adjacent) |
| Signe de les raons trigonomètriques |
π = 180º
]]>
π = 180º
]]>
π = 180º
]]>sin (180º-a) = sin a
cos(180º - a) = - cos a
tg (180º - a) = - tg a
sin(180º + a) = -sin a
cos(180º + a) = -cosa
tg(180º +a) = tg a
sin(-a) = - sina
cos(-a) = cos a
tg(-a) = - tg a
a) #a º
b) #b º
c) #c º
Format: sense unitats
Després aplica:
180º - a pel 2n quadrant
180º + a pel 3r quadrant
360º - a pel quart quadrant
]]>
a) #a º
b) #b º
c) #c º
Format: sense unitats
Després aplica:
180º - a pel 2n quadrant
180º + a pel 3r quadrant
360º - a pel quart quadrant
]]>
a) #a º
b) #b º
c) #c º
Format: sense unitats
Després aplica:
180º - a pel 2n quadrant
180º + a pel 3r quadrant
360º - a pel quart quadrant
]]>Expresseu les raons trigonomètriques dels angles en funció de les d'angles del 1r quadrant (en valor absolut):
|sin #a º| = |sin {#1} º|
|cos #b º| = |cos {#2} º|
|tg #c º| = |tg {#3} º|
| Relació fonamental |
| «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»sin«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»§#945;«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«msup mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»cos«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»§#945;«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«/math» |
|
Se'n dedueix que: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»sin§#945;«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#177;«/mo»«msqrt mathcolor=¨#003300¨»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»-«/mo»«msup»«mi mathvariant=¨bold¨»cos«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mi mathvariant=¨bold¨»§#945;«/mi»«/msqrt»«mspace linebreak=¨newline¨/»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»cos§#945;«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#177;«/mo»«msqrt mathcolor=¨#003300¨»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»-«/mo»«msup»«mi mathvariant=¨bold¨»sin«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mi mathvariant=¨bold¨»§#945;«/mi»«/msqrt»«/mrow»«/mstyle»«/math» Calculadora: si cosα = 0,5 cal escriure: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msqrt/»«mfenced»«mrow»«mn»1«/mn»«mo»-«/mo»«mn»0«/mn»«mo».«/mo»«msup»«mn»5«/mn»«mn»2«/mn»«/msup»«/mrow»«/mfenced»«/math» |
|
Es recorda que: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»tg§#945;«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mfrac mathcolor=¨#003300¨»«mi mathvariant=¨bold¨»sin§#945;«/mi»«mi mathvariant=¨bold¨»cos§#945;«/mi»«/mfrac»«/mrow»«/mstyle»«/math» |
Un cop trobat el cosinus, es recorda que tgx = sinx/cosx
]]>Si es divideix la 1a equació per sin2x:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»+«/mo»«mfrac mathcolor=¨#00007F¨»«mn mathvariant=¨bold¨»1«/mn»«mrow»«msup»«mi mathvariant=¨bold¨»tg«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mi mathvariant=¨bold¨»x«/mi»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mfrac mathcolor=¨#00007F¨»«mn mathvariant=¨bold¨»1«/mn»«mrow»«msup»«mi mathvariant=¨bold¨»sin«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mi mathvariant=¨bold¨»x«/mi»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#8660;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»sinx«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#177;«/mo»«msqrt mathcolor=¨#00007F¨»«mfrac»«mrow»«msup»«mi mathvariant=¨bold¨»tg«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mi mathvariant=¨bold¨»x«/mi»«/mrow»«mrow»«msup»«mi mathvariant=¨bold¨»tg«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfrac»«/msqrt»«/mrow»«/mstyle»«/math»
]]>si es substitueix sinx per tga·cosa:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mfenced mathcolor=¨#00007F¨»«mrow»«msup»«mi mathvariant=¨bold¨»tg«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«msup»«mi mathvariant=¨bold¨»cos«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»+«/mo»«msup mathcolor=¨#00007F¨»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»cos«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»a«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#8660;«/mo»«msup mathcolor=¨#00007F¨»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»cos«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»a«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»(«/mo»«msup mathcolor=¨#00007F¨»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»tg«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»a«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»+«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#8660;«/mo»«msup mathcolor=¨#00007F¨»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»cos«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»a«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mfrac mathcolor=¨#00007F¨»«mn mathvariant=¨bold¨»1«/mn»«mrow»«msup»«mi mathvariant=¨bold¨»tg«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfrac»«/mrow»«/mstyle»«/math»
]]>
sin (90º-a) = cos a
cos(90º - a) = sin a
tg (90º - a) = 1/tg a
sin (180º-a) = sin a
cos(180º - a) = - cos a
tg (180º - a) = - tg a
| Relació fonamental |
| «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»sin«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»§#945;«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«msup mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»cos«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»§#945;«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«/math» |
|
Se'n dedueix que: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»sin§#945;«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#177;«/mo»«msqrt mathcolor=¨#003300¨»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»-«/mo»«msup»«mi mathvariant=¨bold¨»cos«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mi mathvariant=¨bold¨»§#945;«/mi»«/msqrt»«mspace linebreak=¨newline¨/»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»cos§#945;«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#177;«/mo»«msqrt mathcolor=¨#003300¨»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»-«/mo»«msup»«mi mathvariant=¨bold¨»sin«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mi mathvariant=¨bold¨»§#945;«/mi»«/msqrt»«/mrow»«/mstyle»«/math» Calculadora: si cosα = 0,5 cal escriure: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msqrt/»«mfenced»«mrow»«mn»1«/mn»«mo»-«/mo»«mn»0«/mn»«mo».«/mo»«msup»«mn»5«/mn»«mn»2«/mn»«/msup»«/mrow»«/mfenced»«/math» |
|
Es recorda que: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»tg§#945;«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mfrac mathcolor=¨#003300¨»«mi mathvariant=¨bold¨»sin§#945;«/mi»«mi mathvariant=¨bold¨»cos§#945;«/mi»«/mfrac»«/mrow»«/mstyle»«/math» |
a) tg a
b) sin(2a)
Es recorda la fórmula: sin (2a) = 2·sina·cosa
]]>«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»cos«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»a«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#177;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#8201;«/mo»«msqrt mathcolor=¨#000066¨»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»-«/mo»«msup»«mi mathvariant=¨bold¨»sin«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mi mathvariant=¨bold¨»a«/mi»«/msqrt»«mspace linebreak=¨newline¨/»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»tg«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»a«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»=«/mo»«mfrac mathcolor=¨#000066¨»«mi mathvariant=¨bold¨»sina«/mi»«mi mathvariant=¨bold¨»cosa«/mi»«/mfrac»«mspace linebreak=¨newline¨/»«/math»
i fixar-se en el quadrant per determinar els signes.
]]>i pensant que cos(a-b) = cos [a+(-b)]
Determineu l'expressió de:
cos(a-b) = cos{#1}·cos{#2} {#3}sin{#4}·sin{#5}
Format: pel signe, escriu (amb lletres): més o menys
]]>i pensant que sin(a+b) = cos [90º-(a+b)]
Determineu l'expressió de:
sin(a+b) = sin{#1}·cos{#2} {#3}cos{#4}·sin{#5}
Format: pel signe, escriu (amb lletres): més o menys
]]>i pensant que sin(a-b) = sin [a+(-b)]
Determineu l'expressió de:
sin(a-b) = sin{#1}·cos{#2} {#3}cos{#4}·sin{#5}
Format: pel signe, escriu (amb lletres): més o menys
]]>Es resolen fàcilment,
sina = sin(180º-a) = sin(π -a)
cosa = cos (-a)
tga = tg(180º+a) = tg(π+a)
]]>
Format de la resposta: en radiants: π i fraccions de π «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo»{«/mo»«mi mathvariant=¨normal¨»x«/mi»«mo»=«/mo»«mfrac»«mi mathvariant=¨normal¨»§#960;«/mi»«mn»4«/mn»«/mfrac»«mo»+«/mo»«mn»2«/mn»«mi»k§#960;«/mi»«mo»,«/mo»«mi mathvariant=¨normal¨»x«/mi»«mo»=«/mo»«mfrac»«mrow»«mn»3«/mn»«mi mathvariant=¨normal¨»§#960;«/mi»«/mrow»«mn»4«/mn»«/mfrac»«mo»+«/mo»«mn»2«/mn»«mi»k§#960;«/mi»«mo»}«/mo»«/mrow»«/mstyle»«/math»
]]>L'altre angle és π menys el que hem deduït de la taula.
]]>Format de la resposta: en radiants: π i fraccions de π «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo»{«/mo»«mi mathvariant=¨normal¨»x«/mi»«mo»=«/mo»«mfrac»«mi mathvariant=¨normal¨»§#960;«/mi»«mn»4«/mn»«/mfrac»«mo»+«/mo»«mn»2«/mn»«mi»k§#960;«/mi»«mo»,«/mo»«mi mathvariant=¨normal¨»x«/mi»«mo»=«/mo»«mfrac»«mrow»«mn»3«/mn»«mi mathvariant=¨normal¨»§#960;«/mi»«/mrow»«mn»4«/mn»«/mfrac»«mo»+«/mo»«mn»2«/mn»«mi»k§#960;«/mi»«mo»}«/mo»«/mrow»«/mstyle»«/math»
]]>«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»w«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»1«/mn»«/mrow»«/mstyle»«/math» : #G1 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»w«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»2«/mn»«/mrow»«/mstyle»«/math»: #G2
Per tant, les dues solucions són:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfenced mathcolor=¨#00007F¨ open=¨{¨ close=¨¨»«mtable columnalign=¨left¨»«mtr»«mtd»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»w«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»2«/mn»«mi mathvariant=¨bold¨»k§#960;«/mi»«/mtd»«/mtr»«mtr»«mtd»«mi mathvariant=¨bold-italic¨»x«/mi»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»w«/mi»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»2«/mn»«mi mathvariant=¨bold¨»k§#960;«/mi»«/mtd»«/mtr»«/mtable»«/mfenced»«/mstyle»«/math»
Es transformen a positives si cal.
]]>
Format de la resposta: en radiants: π i fraccions de π «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo»{«/mo»«mi mathvariant=¨normal¨»x«/mi»«mo»=«/mo»«mfrac»«mi mathvariant=¨normal¨»§#960;«/mi»«mn»4«/mn»«/mfrac»«mo»+«/mo»«mn»2«/mn»«mi»k§#960;«/mi»«mo»,«/mo»«mi mathvariant=¨normal¨»x«/mi»«mo»=«/mo»«mfrac»«mrow»«mn»3«/mn»«mi mathvariant=¨normal¨»§#960;«/mi»«/mrow»«mn»4«/mn»«/mfrac»«mo»+«/mo»«mn»2«/mn»«mi»k§#960;«/mi»«mo»}«/mo»«/mrow»«/mstyle»«/math»
]]>L'altre angle és π+α
]]>Format del resultat: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mfenced open=¨{¨ close=¨}¨»«mrow»«mi»x«/mi»«mo»=«/mo»«mi mathvariant=¨normal¨»§#960;«/mi»«mo»+«/mo»«mfrac»«mi»k§#960;«/mi»«mn»3«/mn»«/mfrac»«mo»,«/mo»«mi mathvariant=¨normal¨»x«/mi»«mo»=«/mo»«mfrac»«mrow»«mn»3«/mn»«mo»§#183;«/mo»«mi mathvariant=¨normal¨»§#960;«/mi»«/mrow»«mn»2«/mn»«/mfrac»«mo»+«/mo»«mfrac»«mrow»«mi»k«/mi»«mi»§#960;«/mi»«/mrow»«mn»3«/mn»«/mfrac»«/mrow»«/mfenced»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold-italic¨»a«/mi»«mi mathvariant=¨bold-italic¨»n«/mi»«mi mathvariant=¨bold-italic¨»g«/mi»«mi mathvariant=¨bold-italic¨»l«/mi»«mi mathvariant=¨bold-italic¨»e«/mi»«mi mathvariant=¨bold-italic¨»s«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mi mathvariant=¨bold-italic¨»p«/mi»«mi mathvariant=¨bold-italic¨»o«/mi»«mi mathvariant=¨bold-italic¨»s«/mi»«mi mathvariant=¨bold-italic¨»i«/mi»«mi mathvariant=¨bold-italic¨»t«/mi»«mi mathvariant=¨bold-italic¨»i«/mi»«mi mathvariant=¨bold-italic¨»u«/mi»«mi mathvariant=¨bold-italic¨»s«/mi»«mo mathvariant=¨bold¨»)«/mo»«/mrow»«/mstyle»«/math»
]]>«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»w«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»11«/mn»«/mstyle»«/math» : #G1 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»w«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»21«/mn»«/mstyle»«/math»: #G2
Per tant, cal resoldre les dues equacions:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfenced mathcolor=¨#00007F¨ open=¨{¨ close=¨¨»«mtable columnalign=¨left¨»«mtr»«mtd»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»w«/mi»«mn mathvariant=¨bold¨»11«/mn»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»2«/mn»«mi mathvariant=¨bold¨»k§#960;«/mi»«/mtd»«/mtr»«mtr»«mtd»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»w«/mi»«mn mathvariant=¨bold¨»21«/mn»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»2«/mn»«mi mathvariant=¨bold¨»k§#960;«/mi»«/mtd»«/mtr»«/mtable»«/mfenced»«/mstyle»«/math»
]]>«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfenced open=¨{¨ close=¨}¨»«mtable mathcolor=¨#00007F¨ columnalign=¨left¨»«mtr»«mtd»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»w«/mi»«mn mathvariant=¨bold¨»11«/mn»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»2«/mn»«mi mathvariant=¨bold¨»k§#960;«/mi»«/mtd»«/mtr»«mtr»«mtd»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»w«/mi»«mn mathvariant=¨bold¨»21«/mn»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»2«/mn»«mi mathvariant=¨bold¨»k§#960;«/mi»«/mtd»«/mtr»«/mtable»«/mfenced»«mo»§#8660;«/mo»«mfenced open=¨{¨ close=¨}¨»«mtable mathcolor=¨#00007F¨ columnalign=¨left¨»«mtr»«mtd»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»w«/mi»«mn mathvariant=¨bold¨»11«/mn»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold-italic¨»b«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»2«/mn»«mi mathvariant=¨bold¨»k§#960;«/mi»«/mtd»«/mtr»«mtr»«mtd»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»w«/mi»«mn mathvariant=¨bold¨»21«/mn»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold-italic¨»b«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»2«/mn»«mi mathvariant=¨bold¨»k§#960;«/mi»«/mtd»«/mtr»«/mtable»«/mfenced»«mspace linebreak=¨newline¨/»«mo»§#8660;«/mo»«mfenced open=¨{¨ close=¨}¨»«mtable mathcolor=¨#00007F¨ columnalign=¨left¨»«mtr»«mtd»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»=«/mo»«mfrac»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»f«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»§#160;«/mo»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«/mfrac»«mo mathvariant=¨bold¨»+«/mo»«mfrac»«mrow»«mn mathvariant=¨bold¨»2«/mn»«mi mathvariant=¨bold¨»k§#960;«/mi»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«/mfrac»«/mtd»«/mtr»«mtr»«mtd»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»=«/mo»«mfrac»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»f«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«/mfrac»«mo mathvariant=¨bold¨»+«/mo»«mfrac»«mrow»«mn mathvariant=¨bold¨»2«/mn»«mi mathvariant=¨bold¨»k§#960;«/mi»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«/mfrac»«/mtd»«/mtr»«/mtable»«/mfenced»«/mstyle»«/math»
Es transformen els angles a positius si cal.
]]>Format del resultat: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced open=¨{¨ close=¨}¨»«mrow»«mi»x«/mi»«mo»=«/mo»«mi mathvariant=¨normal¨»§#960;«/mi»«mo»+«/mo»«mi»k§#960;«/mi»«mo»,«/mo»«mi mathvariant=¨normal¨»x«/mi»«mo»=«/mo»«mo»-«/mo»«mfrac»«mrow»«mn»3«/mn»«mo»§#183;«/mo»«mi mathvariant=¨normal¨»§#960;«/mi»«/mrow»«mn»2«/mn»«/mfrac»«mo»+«/mo»«mi»k«/mi»«mi»§#960;«/mi»«/mrow»«/mfenced»«/math»
]]>i que #w1 i #w2 (=-#w1)tenen el mateix cosinus,
cal resoldre les dues equacions:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced mathcolor=¨#0000FF¨ open=¨{¨ close=¨¨»«mtable columnalign=¨left¨»«mtr»«mtd»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»w«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»2«/mn»«mi mathvariant=¨bold-italic¨»k«/mi»«mi mathvariant=¨bold-italic¨»§#960;«/mi»«/mtd»«/mtr»«mtr»«mtd»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»w«/mi»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»2«/mn»«mi mathvariant=¨bold-italic¨»k«/mi»«mi mathvariant=¨bold-italic¨»§#960;«/mi»«/mtd»«/mtr»«/mtable»«/mfenced»«/math»
]]>Format del resultat: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mfenced open=¨{¨ close=¨}¨»«mrow»«mi»x«/mi»«mo»=«/mo»«mi mathvariant=¨normal¨»§#960;«/mi»«mo»+«/mo»«mi»k§#960;«/mi»«mo»,«/mo»«mi mathvariant=¨normal¨»x«/mi»«mo»=«/mo»«mfrac»«mrow»«mn»3«/mn»«mo»§#183;«/mo»«mi mathvariant=¨normal¨»§#960;«/mi»«/mrow»«mn»2«/mn»«/mfrac»«mo»+«/mo»«mi»k«/mi»«mi»§#960;«/mi»«/mrow»«/mfenced»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold-italic¨»a«/mi»«mi mathvariant=¨bold-italic¨»n«/mi»«mi mathvariant=¨bold-italic¨»g«/mi»«mi mathvariant=¨bold-italic¨»l«/mi»«mi mathvariant=¨bold-italic¨»e«/mi»«mi mathvariant=¨bold-italic¨»s«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mi mathvariant=¨bold-italic¨»p«/mi»«mi mathvariant=¨bold-italic¨»o«/mi»«mi mathvariant=¨bold-italic¨»s«/mi»«mi mathvariant=¨bold-italic¨»i«/mi»«mi mathvariant=¨bold-italic¨»t«/mi»«mi mathvariant=¨bold-italic¨»i«/mi»«mi mathvariant=¨bold-italic¨»u«/mi»«mi mathvariant=¨bold-italic¨»s«/mi»«mo mathvariant=¨bold¨»)«/mo»«/mrow»«/mstyle»«/math»
]]>«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»w«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»1«/mn»«/mrow»«/mstyle»«/math» : #G1 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»w«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»2«/mn»«/mrow»«/mstyle»«/math»: #G2
Per tant, cal resoldre les dues equacions:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfenced mathcolor=¨#00007F¨ open=¨{¨ close=¨¨»«mtable columnalign=¨left¨»«mtr»«mtd»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»w«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»2«/mn»«mi mathvariant=¨bold¨»k§#960;«/mi»«/mtd»«/mtr»«mtr»«mtd»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»w«/mi»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»2«/mn»«mi mathvariant=¨bold¨»k§#960;«/mi»«/mtd»«/mtr»«/mtable»«/mfenced»«/mstyle»«/math»
]]>«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfenced open=¨{¨ close=¨}¨»«mtable mathcolor=¨#00007F¨ columnalign=¨left¨»«mtr»«mtd»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»w«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»2«/mn»«mi mathvariant=¨bold¨»k§#960;«/mi»«/mtd»«/mtr»«mtr»«mtd»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»w«/mi»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»2«/mn»«mi mathvariant=¨bold¨»k§#960;«/mi»«/mtd»«/mtr»«/mtable»«/mfenced»«mo»§#8660;«/mo»«mfenced open=¨{¨ close=¨}¨»«mtable mathcolor=¨#00007F¨ columnalign=¨left¨»«mtr»«mtd»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»w«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold-italic¨»b«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»2«/mn»«mi mathvariant=¨bold¨»k§#960;«/mi»«/mtd»«/mtr»«mtr»«mtd»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»w«/mi»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold-italic¨»b«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»2«/mn»«mi mathvariant=¨bold¨»k§#960;«/mi»«/mtd»«/mtr»«/mtable»«/mfenced»«mspace linebreak=¨newline¨/»«mfenced open=¨{¨ close=¨}¨»«mtable mathcolor=¨#00007F¨ columnalign=¨left¨»«mtr»«mtd»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»=«/mo»«mfrac»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»f«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»§#160;«/mo»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«/mfrac»«mo mathvariant=¨bold¨»+«/mo»«mfrac»«mrow»«mn mathvariant=¨bold¨»2«/mn»«mi mathvariant=¨bold¨»k§#960;«/mi»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«/mfrac»«/mtd»«/mtr»«mtr»«mtd»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»=«/mo»«mfrac»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»f«/mi»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»§#160;«/mo»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«/mfrac»«mo mathvariant=¨bold¨»+«/mo»«mfrac»«mrow»«mn mathvariant=¨bold¨»2«/mn»«mi mathvariant=¨bold¨»k§#960;«/mi»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«/mfrac»«/mtd»«/mtr»«/mtable»«/mfenced»«/mstyle»«/math»
]]>Format del resultat: {x=31+90k,x=320+90k} graus arrodonits sense unitats i positius (suma 360º, si cal)
]]>
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»w«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»1«/mn»«/mrow»«/mstyle»«/math»º : #G1 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»w«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#176;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»180«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#186;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#00007F¨»w«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»)«/mo»«/mstyle»«/math»: #G2
Cal resoldre les dues equacions:
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cal resoldre les dues equacions:
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cal resoldre les dues equacions:
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