# Precalculus : Trigonometric Functions

## Example Questions

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### Example Question #57 : Fundamental Trigonometric Identities

Which of the following trigonometric identities is INCORRECT?

Possible Answers:     Correct answer: Explanation:

Cosine and sine are not reciprocal functions. and ### Example Question #58 : Fundamental Trigonometric Identities

Using the trigonometric identities prove whether the following is valid: Possible Answers:

False

Uncertain

True

Only in the range of: Only in the range of: Correct answer:

True

Explanation:

We begin with the left-hand side of the equation and utilize basic trigonometric identities, beginning with converting the inverse functions to their corresponding base functions: Next, we rewrite the fractional division in order to simplify the equation: In fractional division we multiply by the reciprocal as follows: If we reduce the fraction using basic identities we see that the equivalence is proven:  ### Example Question #59 : Fundamental Trigonometric Identities

Which of the following identities is incorrect?

Possible Answers:     Correct answer: Explanation:

The true identity is because cosine is an even function.

### Example Question #60 : Fundamental Trigonometric Identities

State in terms of sine and cosine.

Possible Answers:     Correct answer: Explanation:

The definition of tangent is sine divided by cosine. ### Example Question #61 : Fundamental Trigonometric Identities Possible Answers:     Correct answer: Explanation:

Using these basic identities:   we find the original expression to be which simplifies to .

Further simplifying: The cosines cancel, giving us ### Example Question #62 : Fundamental Trigonometric Identities

Which of the following is the best answer for ?

Possible Answers:     Correct answer: Explanation:

Write the Pythagorean identity. Substract from both sides. The other answers are incorrect.

### Example Question #63 : Fundamental Trigonometric Identities

Express in terms of only sines and cosines.

Possible Answers:     Correct answer: Explanation:

The correct answer is . Begin by substituting  , and . This gives us: .

### Example Question #171 : Trigonometric Functions

Express in terms of only sines and cosines.

Possible Answers:     Correct answer: Explanation:

To solve this problem, use the identities   , and . Then we get   1 2 10 11 12 13 14 15 16 18 Next →

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