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Problem: 19 Set: Exercises Page: 427Look in your textbook for this problem statement.Step 1Suppose = /4.

Step 2Replace with /4.

Step 3Evaluate.

This is an inequality. Therefore the equation is not an identity. One counterexample is = /4 or 45 .

Problem: 21 Set: Exercises Page: 427Look in your textbook for this problem statement.Step 1Suppose x= /4.

Step 2Replace xwith /4.

Step 3Evaluate.

This is an inequality. Therefore the equation is not an identity. One counterexample is x= /4 or 45 .

Problem: 23 Set: Exercises Page: 427Look in your textbook for this problem statement.Step 1Suppose A = /4.

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Step 2Replace A with /4.

Step 3Evaluate.

This is an inequality. Therefore the equation is not an identity. One counterexample is A = /4 or 45 .

Problem: 25 Set: Exercises Page: 428Look in your textbook for this problem statement.Step 1

Choose an identity that involves sin and csc .

Step 2Substitute 2/5 for sin .

Step 3

Evaluate.

Problem: 27 Set: Exercises Page: 428Look in your textbook for this problem statement.Step 1Choose a Pythagorean identity that involves sin and cos .

Step 2Substitute 1/4 for sin .

Step 3Evaluate.

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Take the square root of each side.

Step 4 is an angle in Quadrant I. Therefore cos is positive.

Problem: 29 Set: Exercises Page: 428Look in your textbook for this problem statement.Step 1Choose a Pythagorean identity that involves csc and cot .

Step 2

Step 3Evaluate.

Take the square root of each side.

Step 4 is an angle in Quadrant II. Therefore cot is negative.

Problem: 31 Set: Exercises Page: 428Look in your textbook for this problem statement.Step 1Since there are no identities relating sin and tan , we use two identities, one relating sin and cos andanother relating sin , cos , and tan .

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Step 2Choose a Pythagorean identity that involves sin and cos .

Step 3Substitute 1/3 for sin .

Step 4Evaluate.

Take the square root of each side.

Step 5 is an angle in Quadrant III. Therefore cos is negative.

Step 6Now find tan using a quotient identity.

Step 7Substitute 1/3 for sin and 2( 2)/3 for cos .

Step 8Evaluate.

Problem: 33 Set: Exercises Page: 428Look in your textbook for this problem statement.Step 1

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Since there are no identities relating sec and sin , we use two identities, one relating sec and cos andanother relating cos , and sin .

Step 2Use a reciprocal identity.

Step 3Substitute 7/5 for sec .

Step 4Evaluate.

Step 5Choose a Pythagorean identity that involves sin and cos .

Step 6Substitute 5/7 for cos .

Step 7Evaluate.

Take the square root of each side.

Step 8 is an angle in Quadrant III. Therefore sin is negative.

Problem: 35 Set: Exercises Page: 428Look in your textbook for this problem statement.Step 1

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Since there are no identities relating cot and sin , we use two identities, one relating cot and csc andanother relating csc , and sin .

Step 2Choose a Pythagorean identity.

Step 3Substitute 4/3 for cot .

Step 4Evaluate.

Take the square root of each side.

Step 5 is an angle in Quadrant IV. Therefore csc is negative.

Step 6Use a reciprocal identity.

Step 7Substitute 5/3 for csc .

Step 8Evaluate.