1MA 04. VECTORS/1MA.04.1 Definicions 1MA.04.1.24Q MòdulArgument Quin és el mòdul i l'argument del vector «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mover mathcolor=¨#003300¨»«mi mathvariant=¨bold¨»v«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«/mstyle»«/math»? Fixa't en el quadrant!

Format de la resposta:

Mòdul: Fracció o arrel simplificada

35º (arrodonit a la unitat).

]]> El vector és:

#G1

]]> 1.0000000 0.5000000 0 0 mòdul =#sol1argument =#sol2]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>aleatori</mi><mfenced><mrow><mn>2</mn><mo>,</mo><mn>7</mn></mrow></mfenced><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mfrac><mi>a2</mi><mi>a1</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>a1</mi><mo>,</mo><mi>a2</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><msqrt><mrow><msup><mi>a1</mi><mn>2</mn></msup><mo>+</mo><msup><mi>a2</mi><mn>2</mn></msup></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m1</mi><mo>=</mo><mi>atan</mi><mo>(</mo><mi>c</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m2</mi><mo>=</mo><mfrac><mrow><mi>m1</mi><mo>*</mo><mn>180</mn></mrow><pi/></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m3</mi><mo>=</mo><mfenced close="|" open="|"><mrow><mi>arrodoneix</mi><mo>(</mo><mi>m2</mi><mo>)</mo></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a1</mi><mo>></mo><mn>0</mn></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a2</mi><mo>></mo><mn>0</mn></mrow><mtable><mtr><mtd><mi>Q</mi><mo>=</mo><mo>"</mo><mn>1</mn><mi>r</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>Q2</mi><mo>=</mo><mo>"</mo><mi>entre</mi><mo> </mo><mn>0</mn><mo> </mo><mi>i</mi><mo> </mo><mn>90</mn><mo>°</mo><mo>"</mo></mtd></mtr><mtr><mtd><mi>Q3</mi><mo>=</mo><mo>"</mo><mi>α</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>sol2</mi><mo>=</mo><mi>m3</mi><csymbol definitionURL="http://.../units/degree/angular">°</csymbol></mtd></mtr><mtr><mtd/></mtr></mtable><mtable><mtr><mtd><mi>Q</mi><mo>=</mo><mo>"</mo><mn>4</mn><mi>t</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>Q2</mi><mo>=</mo><mo>"</mo><mi>entre</mi><mo> </mo><mn>270</mn><mo>°</mo><mo> </mo><mi>i</mi><mo> </mo><mn>360</mn><mo>°</mo><mo>"</mo></mtd></mtr><mtr><mtd><mi>Q3</mi><mo>=</mo><mo>"</mo><mn>360</mn><mo>°</mo><mo>-</mo><mfenced close="|" open="|"><mi>α</mi></mfenced><mo>"</mo></mtd></mtr><mtr><mtd><mi>sol2</mi><mo>=</mo><mn>360</mn><csymbol definitionURL="http://.../units/degree/angular">°</csymbol><mo>-</mo><mi>m3</mi><csymbol definitionURL="http://.../units/degree/angular">°</csymbol></mtd></mtr></mtable></apply><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a2</mi><mo>></mo><mn>0</mn></mrow><mtable><mtr><mtd><mi>Q</mi><mo>=</mo><mo>"</mo><mn>2</mn><mi>n</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>Q2</mi><mo>=</mo><mo>"</mo><mi>entre</mi><mo> </mo><mn>90</mn><mo>°</mo><mo> </mo><mi>i</mi><mo> </mo><mn>180</mn><mo>°</mo><mo>"</mo></mtd></mtr><mtr><mtd><mi>Q3</mi><mo>=</mo><mo>"</mo><mn>180</mn><mo>°</mo><mo>-</mo><mfenced close="|" open="|"><mi>α</mi></mfenced><mo>"</mo></mtd></mtr><mtr><mtd><mi>sol2</mi><mo>=</mo><mn>180</mn><csymbol definitionURL="http://.../units/degree/angular">°</csymbol><mo>-</mo><mi>m3</mi><csymbol definitionURL="http://.../units/degree/angular">°</csymbol></mtd></mtr><mtr><mtd/></mtr></mtable><mtable><mtr><mtd><mi>Q</mi><mo>=</mo><mo>"</mo><mn>3</mn><mi>r</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>Q2</mi><mo>=</mo><mo>"</mo><mi>entre</mi><mo> </mo><mn>180</mn><mo>°</mo><mo> </mo><mi>i</mi><mo> </mo><mn>270</mn><mo>°</mo><mo>"</mo></mtd></mtr><mtr><mtd><mi>Q3</mi><mo>=</mo><mo>"</mo><mn>180</mn><mo>°</mo><mo>+</mo><mi>α</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>sol2</mi><mo>=</mo><mn>180</mn><csymbol definitionURL="http://.../units/degree/angular">°</csymbol><mo>+</mo><mi>m3</mi><csymbol definitionURL="http://.../units/degree/angular">°</csymbol></mtd></mtr></mtable></apply></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T1</mi><mo>=</mo><mi>tauler</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>mostrar_eixos</mi><mo>=</mo><mi>fals</mi></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mi>v</mi><mo>,</mo><mi>punt</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>html_darkblue</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>3</mn></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>,</mo><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mn>4</mn><mo>,</mo><mo>-</mo><mn>5</mn></mrow></mfenced><mo>,</mo><msqrt><mn>41</mn></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mfrac><mn>5</mn><mn>4</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>0.89606</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>51.34</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>51</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>4t</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>entre</ms><mo> </mo><ms>270</ms><mo>°</mo><mo> </mo><ms>i</ms><mo> </mo><ms>360</ms><mo>°</mo></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>360</ms><mo>°</mo><mo>-</mo><mfenced close="|" open="|"><mi>α</mi></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tauler1</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">m</mi><mi>ò</mi><mi>d</mi><mi>u</mi><mi mathvariant="normal">l</mi><mo> </mo><mo>=</mo><mo>#</mo><mi mathvariant="normal">s</mi><mi>o</mi><mi mathvariant="normal">l</mi><mn>1</mn><mspace linebreak="newline"/><mi>a</mi><mi>r</mi><mi mathvariant="normal">g</mi><mi>u</mi><mi mathvariant="normal">m</mi><mi mathvariant="normal">e</mi><mi>n</mi><mi>t</mi><mo> </mo><mo>=</mo><mo>#</mo><mi mathvariant="normal">s</mi><mi>o</mi><mi mathvariant="normal">l</mi><mn>2</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", $, ¥, €, £, kr, Fr, ₩, ₹, руб, BTC, %, ‰, A, K, mol, cd, rad, sr, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> L'argument és l'arc tangent de la segona component dividida per la primera:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#945;«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»arc«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»tg«/mi»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfrac»«/mstyle»«/math»

#G1

Si et fixes en el signe de les components, l'angle està en el #Q quadrant, o sigui #Q2. Es calcula doncs amb: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»Q«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«/mrow»«/mstyle»«/math»

]]>