# 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

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