Precalculus : Find the value of any of the six trigonometric functions of special angles

Study concepts, example questions & explanations for Precalculus

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Example Questions

Example Question #33 : Trigonometric Functions

In a 3-4-5 right triangle, which of the following is a possible value for ?

Possible Answers:

Correct answer:

Explanation:

Sine theta is defined as the leg opposite to the angle over the hypothenuse. Write the definition of sine.  The hypotenuse is the longest side of the right triangle, which indicates that 5 should be in the denominator.

The ratio of the legs opposite to theta over the hypothenuse can either be  or .

 

Example Question #34 : Trigonometric Functions

Find the value of .

Possible Answers:

Correct answer:

Explanation:

Since

we begin by finding the value of .

.

Then, 

Example Question #1 : Find The Value Of Any Of The Six Trigonometric Functions Of Special Angles

Determine the value of:  

Possible Answers:

Correct answer:

Explanation:

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

Example Question #2 : Find The Value Of Any Of The Six Trigonometric Functions Of Special Angles

Find the value of , if possible.

Possible Answers:

Correct answer:

Explanation:

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

Example Question #3 : Find The Value Of Any Of The Six Trigonometric Functions Of Special Angles

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 #4 : Find The Value Of Any Of The Six Trigonometric Functions Of Special Angles

Determine 

Possible Answers:

Correct answer:

Explanation:

Remember that:

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