Secondary Math II
HW 7H-2 Trig sum and difference
Name:_________________________________
Period:__________
Write out the sum or difference identities
sin(u + v) = __________________________________________________
sin(u - v) = __________________________________________________
cos(u + v) = __________________________________________________
cos(u - v) = __________________________________________________
tan(u + v) = __________________________________________________
tan(u - v) = __________________________________________________
Express the angle as a sum or difference of 2 special angles.
1. 15 °
2. 75 °
3. 120 °
Use the sum or difference identity to find an exact value.
5. tan15°
6. sin75°
7. cos75°
8. sin135°
9. sin105°
10. tan105°
11. cos15°
12. tan120°
4. 105 °
Write as a function of one angle.
13. sin40°cos30° + cos40°sin30°
14. cos15°cos25° - sin15°sin25°
15. sin50°cos10° - cos50°sin10°
16.
tan19° + tan 47°
1- tan19°× tan 47°
17. cos38 cos37  sin 38 sin 37
18.
tan7° + tan18°
1- tan7°× tan18°
Prove the identity:
(
)
19. sin x - 90 = -cos x
21. tan(q + 45°) =
1+ tanq
1- tanq
20. cos(x - 90) = sin x
22. cos(x - y) + cos(x + y) = 2cos xcos y
Answers:
1. 45  30 or 60  45
3. 60+60
5. 2  3
7.
9.
11.
13.
15.
17.
19.
21.
6 2
4
2 6
4
2 6
4
sin 70
sin 40
cos1
sin( x  90)  sin x cos90  cos x sin 90  sin x  0  cos x 1   cos x
tan   tan 45
tan   1 1  tan 
tan(  45) 


1  tan  tan 45 1  tan  1 1  tan 