HLRGAATPreISM_35799X_09_ch9

HLRGAATPreISM_35799X_09_ch9 - Chapter 9 Trigonometric...

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Chapter 9: Trigonometric Identities and Equations 9.1: T r igonometr ic Identities 1. Since by the negative-number identities the function is : Odd. 2. Since by the negative-number identities the function is : Even. 3. Since by the negative-number identities the function is : Odd. 4. Since by the negative-number identities the function is : Odd. 5. Since by the negative-number identities the function is : Even. 6. Since by the negative-number identities the function is : Odd. 7. By a quotient identity, therefore B. 8. By a quotient identity, therefore D. 9. By a negative-number identity, , therefore E. 10. By a pythagorean identity, , therefore C. 11. By a pythagorean identity, , therefore A. 12. Using a quotient identity, , therefore C. 13. Using a pythagorean identity and then a quotient identity, therefore A. 14. Using two reciprocal identities and then a quotient identity, therefore E. 15. Using a pythagorean identity, , therefore D. 16. Using a reciprocal identity, therefore B. 17. By a negative-number identity, if . 18. By a negative-number identity, if . 19. By a negative-number identity, if 20. By a negative-number identity, if 21. By a negative-number identity, if 22. By a negative-number identity, if 23. The correct identity is the function must have the argument “ x ” or 24. The square root of a sum does not equal the sum of the square roots: 25. sin in terms of cot sin in terms of sec 2 sec 2 u 1 sec u sin u cos u sin u cos u cos u tan u 1 sec u 1 2 sec 2 u 1 2 u : u sin u 1 csc u 1 2 1 cot 2 u 2 1 cot 2 u 1 cot 2 u u : u 2 a 2 b 2 2 a 2 2 b 2 , so 2 sin 2 u cos 2 u sin u cos u . u , t , etc. 1 cot 2 x csc 2 x ; cot 1 u 2 cot u , then cot a 4 π 7 b cot 4 π 7 . tan 1 u 2 tan u , then tan a π 7 b tan π 7 . sin 1 u 2 sin u , then sin 1 2.5 2 sin 2.5. sin 1 u 2 sin u , then sin 1 .5 2 sin .5. cos 1 u 2 cos u , then cos 1 5.46 2 cos 5.46 cos 1 u 2 cos u , then cos 1 4.38 2 cos 4.38 cos 2 x 1 sec 2 x , 1 sin 2 x 1 csc 2 x cot 2 x 2 sin 2 x sin x cos x tan x , sec x csc x 1 cos x 1 sin x sec 2 x 1 tan 2 x sin 2 x cos 2 x , tan x cos x sin x cos x cos x 1 sin x sin 1 x 2 1 sin 2 x cos 2 x tan 2 x 1 sec 2 x cos 1 x 2 cos x tan x sin x cos x , cos x sin x cot x , csc x csc 1 x 2 , sec x sec 1 x 2 , cot x cot 1 x 2 , tan x tan 1 x 2 , cos x cos 1 x 2 , sin x sin 1 x 2 ,
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26. cos in terms of sin cos in terms of cot cos in terms of csc 27. tan in terms of sin tan in terms of cos tan in terms of sec tan in terms of csc 28. cot in terms of sin cot in terms of cos cot in terms of csc 29. sec in terms of sin sec in terms of tan sec in terms of cot sec in terms of csc 30. csc in terms of cos csc in terms of tan csc in terms of cot csc in terms of sec 31. 32. 33. sin b tan b cos b sin b cos b tan b tan b tan b tan 2 b cot a sin a cos a sin a sin a 1 cos a tan u cos u sin u cos u cos u 1 sin u csc u 2 tan 2 u 1 tan u sec u 2 sec 2 u 1 sec u 2 sec 2 u 1 sec 2 u 1 u : u csc u 2 1 cot 2 u u : u B tan 2 u 1 tan 2 u 2 tan 2 u 1 tan u B 1 1 tan 2 u csc u 2 1 cot 2 u u : u csc u 1 sin u 1 2 1 cos 2 u 2 1 cos 2 u 1 cos 2 u u : u 2 csc 2 u 2 csc 2 u 1 csc u 2 csc 2 u 1 csc u 2 csc 2 u 1 csc 2 u 1 1 B 1 1 csc 2 u 1 B csc 2 u 1 csc 2 u sec u 1 cos u 1 2
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