Find the exact value of the trigonometric function at the given real number

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Found in: Page 417

Book edition 7th Edition

Author(s) James Stewart, Lothar Redlin, Saleem Watson

Pages 948 pages

ISBN 9781337067508

Short Answer

Find the exact value of the trigonometric function at the given real number.a. b. c.

a. The exact value of the trigonometric function .

b. The exact value of the trigonometric function .

c. The exact value of the trigonometric function .

See the step by step solution

Step by Step Solution

Part a. Step 1. Find the reference number.

Part a. Step 3. Find the value.

The value of the trigonometric function of is the same, except possibly for sign, as the value of the trigonometric function of . The corresponding terminal point for is in the first quadrant.

Therefore, the exact value of the trigonometric function .

Part b. Step 1. Find the reference number.

The reference number associated with , a real number is the shortest distance along the unit circle between the terminal point determined by and the -axis.

Here, , which lies in quadrant III.

Since lies in quadrant III, therefore, the reference number will be . Here substitute for and simplify for .

Part b. Step 3. Find the value.

The value of the trigonometric function of is the same, except possibly for sign, as the value of the trigonometric function of . The corresponding terminal point for is in the first quadrant.

Therefore, the exact value of the trigonometric function .

Part c. Step 1. Find the reference number.

The reference number associated with , a real number is the shortest distance along the unit circle between the terminal point determined by and the -axis.

Here, , which lies in quadrant IV.

Since lies in quadrant IV, therefore, the reference number will be . Here substitute for and simplify for .

Part c. Step 3. Find the value.

The value of the trigonometric function of is the same, except possibly for sign, as the value of the trigonometric function of . The corresponding terminal point for is in the first quadrant.

Therefore, the exact value of the trigonometric function .

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