Pre-Calc/Trig Unit 3: Analytic Trig and Applications/5.1 Fundamental Identities Use the fundamental identities to find the value of the trigonometric ... Use the fundamental identities to find the value of the trigonometric function.

Find csc θ if sin θ = -  and θ is in quadrant IV.

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]]> Use the fundamental identities to find the value of the trigonometric ... Use the fundamental identities to find the value of the trigonometric function.

Find cos θ if sin θ = -  and θ is in quadrant III.

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]]> - 

]]> 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 Correct. 

]]> - 

]]> 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 Incorrect.  Try one of the Pythagorean Identities.

]]>

]]> 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 Incorrect.  Try one of the Pythagorean Identities.

]]> Write the expression in terms of sine and cosine, and simplify so that no ... Write the expression in terms of sine and cosine, and simplify so that no quotients appear in the final expression.

]]> 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 1.0000000 0.3333333 0 true true abc sec x

]]> Correct

]]> csc x

]]> Incorrect.  Think "Pythagorean Identity".

]]> 1

]]> Incorrect.  Think "Pythagorean Identity".

]]> -sec x

]]> Incorrect.  Think "Pythagorean Identity".

]]> Write the expression in terms of sine and cosine, and simplify so that no ... Write the expression in terms of sine and cosine, and simplify so that no quotients appear in the final expression.

]]> 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 1.0000000 0.3333333 0 true true abc sec² x

]]> Incorrect.  Re-write in terms of sin and cos, then simplify.

]]> cot² x

]]> Correct

]]> csc² x

]]> Incorrect.  Re-write in terms of sin and cos, then simplify.

]]> 1

]]> Incorrect.  Re-write in terms of sin and cos, then simplify.

]]>