Precalculus : Trigonometric Functions

Study concepts, example questions & explanations for Precalculus

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Example Questions

Example Question #16 : Find The Value Of Any Of The Six Trigonometric Functions

Find the value of .

Possible Answers:

Correct answer:

Explanation:

Since

we begin by finding the value of .

.

Then, 

Example Question #17 : Find The Value Of Any Of The Six Trigonometric Functions

Determine the value of:  

Possible Answers:

Correct answer:

Explanation:

To determine the value of , simplify cotangent into sine and cosine.

Example Question #18 : Find The Value Of Any Of The Six Trigonometric Functions

Find the value of , if possible.

Possible Answers:

Correct answer:

Explanation:

In order to solve , split up the expression into 2 parts.

Example Question #19 : Find The Value Of Any Of The Six Trigonometric Functions

Compute , if possible.

Possible Answers:

Correct answer:

Explanation:

Rewrite the expression in terms of cosine.

Evaluate the value of , which is in the fourth quadrant.

Substitute it back to the simplified expression of .

Example Question #20 : Find The Value Of Any Of The Six Trigonometric Functions

Determine 

Possible Answers:

Correct answer:

Explanation:

Remember that:

Example Question #21 : Find The Value Of Any Of The Six Trigonometric Functions

What is the value of ?

Possible Answers:

Correct answer:

Explanation:

The sine of an angle corresponds to the y-component of the triangle in the unit circle.  The angle  is a special angle.  In the unit circle, the hypotenuse is the radius of the unit circle, which is 1.  Since the angle is , the triangle is an isosceles right triangle, or a 45-45-90.  

Use the Pythagorean Theorem to solve for the leg. Both legs will be equal to each other.

Rationalize the denominator.

Therefore, .

Example Question #1 : Prove Trigonometric Identities

Simplify:  

Possible Answers:

Correct answer:

Explanation:

To simplify , find the common denominator and multiply the numerator accordingly.

The numerator is an identity.

Substitute the identity and simplify.

 

Example Question #2 : Prove Trigonometric Identities

Evaluate in terms of sines and cosines:  

Possible Answers:

Correct answer:

Explanation:

Convert  into its sines and cosines.

Example Question #3 : Prove Trigonometric Identities

Simplify the following:

Possible Answers:

The expression is already in simplified form

Correct answer:

Explanation:

First factor out sine x.

Notice that a Pythagorean Identity is present.

The identity needed for this problem is: 

Using this identity the equation becomes,

.

 

Example Question #4 : Prove Trigonometric Identities

Simplify the expression 

 

Possible Answers:

Correct answer:

Explanation:

To simplify, use the trigonometric identities  and  to rewrite both halves of the expression:

Then combine using an exponent to simplify:

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