Precalculus : Use Odd-Even Identities

Study concepts, example questions & explanations for Precalculus

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Example Questions

Example Question #1 : Fundamental Trigonometric Identities

Which of the following statements is false?

Possible Answers:

 

Correct answer:

Explanation:

Of the six trigonometric functions, four are odd, meaning . These four are:

  • sin x
  • tan x
  • cot x
  • csc x

That leaves two functions which are even, which means that . These are:

  • cos x
  • sec x

Of the aforementioned, only  is incorrect, since secant is an even function, which implies that 

Example Question #2 : Fundamental Trigonometric Identities

Find the value of .

Possible Answers:

Correct answer:

Explanation:

Rewrite  by odd and even identities.

Use the difference identity of sine, and choose the special angles 45 and 30, since their difference equals to 15.

Example Question #3 : Fundamental Trigonometric Identities

Simplify:  

Possible Answers:

Correct answer:

Explanation:

Write the even and odd identities for sine and cosine.

Rewrite the expression  and evaluate.

Example Question #4 : Fundamental Trigonometric Identities

Simplify:  

Possible Answers:

Correct answer:

Explanation:

In order to simplify , rewrite the expression after applying the rule of odd-even identities for the secant function.

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