University:
Williams College
Course:
MATH 102 | Foundations in Quantitative Skills
Academic year:

2021
Views:

156

Pages:

4
Author:

Declan Olsen

Advanced Math Trigonometric Identities Quiz Review Name Use Trigonometric Identities to write each expression in terms of a single trigonometric identity or a constant. 1. cot 𝜃 sin 𝜃 2. 1 − sin2 𝜃 cos2 𝜃 1.)_________________ 2.)_________________ 3. 1 − sin2 𝜃 sin2 𝜃 4. sin 𝜃 sec 𝜃 3.)_________________ 4.)_________________ 5. cos 𝜃 sec 𝜃 6. csc 𝜃 sin 𝜃 5.)_________________ 6.)_________________ 1 Use Trigonometric Identities to write each expression in terms of a single trigonometric identity or a constant. 7. tan 𝜃 cos 𝜃 sin 𝜃 8. tan 𝜃 7.)_________________ cot 𝜃 8.)_________________ 9. cos 𝜃 csc 𝜃 tan 𝜃 10. cos 𝜃 csc 𝜃 cot 𝜃 9.)_________________ 10.)________________ 11. sin2 𝜃 1 + cos 𝜃 12. cos 𝜃 + sin2 𝜃 cos 𝜃 11.)________________ 12.)________________ 13. tan 𝜃cos2 𝜃 + tan 𝜃sin2 𝜃 14. sec 2 𝜃 (1 − sin2 𝜃 ) 13.)________________ 14.)________________ 2 Verify the identity. 15. sec 𝜃 cot 𝜃 = csc 𝜃 17. 19. csc 𝜃 cot 𝜃 = sec 𝜃 sec2 𝜃 − 1 sec2 𝜃 = sin2 𝜃 16. sin 𝜃 ∙ 1 csc 𝜃 = sin2 𝜃 18. cos 2 𝜃(1 + tan2 𝜃) = 1 20. tan2 𝜃 ∙ csc 2 𝜃 = sec 2 𝜃 3 Verify the identity. 21. 23. 1 cos 𝜃 − cos 𝜃 = sin 𝜃 tan 𝜃 tan2 𝜃 − 1 tan 𝜃 − 1 22. = tan 𝜃 + 1 sin2 𝜃 − cos2 𝜃 sin 𝜃 + cos 𝜃 24. 1 − 25. (1 − sin 𝜃 )(1 + sin 𝜃 ) = 1 sec2 𝜃 1 sec2 𝜃 = sin 𝜃 − cos 𝜃 = sin2 𝜃 26. 2cos 2 𝜃 − 1 = 1 − 2sin2 𝜃 Answers: 1. cos 𝜃 2. 1 3. cot 2 𝜃 4. tan 𝜃 5. cos 2 𝜃 6. 1 7. 1 8. tan2 𝜃 9. 1 10. cot 2 𝜃 11. 1 − cos 𝜃 12. sec 𝜃 13. tan 𝜃 14. 1 4