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Trigonometric Identities Overview Chapter Exam

Exam Instructions:

Choose your answers to the questions and click 'Next' to see the next set of questions. You can skip questions if you would like and come back to them later with the yellow "Go To First Skipped Question" button. When you have completed the practice exam, a green submit button will appear. Click it to see your results. Good luck!

Page 1

Question 1 1. What's the value of 2sin(θ)cos(θ) given that the equation below is true?

Question 2 2. What is the value of cos(θ) given that the equation below is true?

Question 3 3. Simplify the following expression.

Question 4 4. Which of the following is the alternate definition for tangent?

Question 5 5. What is (1 - cos (90))/(1 + cos (90))?

Page 2

Question 6 6. What is 1/sec (180)?

Question 7 7. What does (1 + cos x)/2 equal?

Question 8 8. How many half-angle identities are there?

Question 9 9. What does sin^2 (x/2) + cos^2 (x/2) equal?

Question 10 10. Prove that (sin (2x))/2 = sin (x) cos (x).

Page 3

Question 11 11.

Which of the following equals cos^2 (x) - sin^2 (x)?

A: cos (2x)

B: sin (2x)

C: 2 cos^2(x) - 1

Question 12 12. Which of the following is an example of a double angle?

Question 13 13. Which of the double-angle identities is used to derive all of the half-angle identities?

Question 14 14. Which identities are used to derive the double-angle identities?

Question 15 15. What do you do to the sum identities to derive the double-angle identities?

Page 4

Question 16 16. How many product-to-sum identities are there?

Question 17 17.

What are the uses of these trig identities?

A: Simplify problems.

B: Prove statements.

C: Define multiplication.

Question 18 18. Prove sin (x + y) = 2 sin (x) cos (y) - sin (x - y).

Question 19 19. Which of the following is not a possible sum or subtraction combination for our sum-to-product identities?

Question 20 20. Prove that the sin (20) + sin (20) = 2 sin (20).

Page 5

Question 21 21.

Which of the following trig functions are part of the sum-to-product identities?

A: sine

B: cosine

C: tangent

Question 22 22. Which function is the reciprocal of cosine?

Question 23 23. The cosecant function is equal to which of the following?

Question 24 24.

Simplify.

sin (theta) csc (theta) cos (theta) = ?

Question 25 25. What does sin^2 (x) + cos^2 (x) always equal?

Page 6

Question 26 26. What does csc2 (75) - cot2 (75) equal?

Question 27 27. Which theorem are the Pythagorean identities based on?

Question 28 28. How many sum and difference identities are there in total?

Question 29 29. Evaluate.

Question 30 30. Evaluate.

Trigonometric Identities Overview Chapter Exam Instructions

Choose your answers to the questions and click 'Next' to see the next set of questions. You can skip questions if you would like and come back to them later with the yellow "Go To First Skipped Question" button. When you have completed the practice exam, a green submit button will appear. Click it to see your results. Good luck!

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