Precalculus: Sine/Cosine Sum & Difference WS
cos( + ) = cos cos
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sin( + ) = sin cos
+ cos sin
cos( − ) = cos cos + sin sin
sin( − ) = sin cos
Recognize the formulas to simplify the expression COMPLETELY. NO calculator!
1. sin 1° cos 2° + cos 1° sin 2°
2. sin 20° cos 15° − cos 20° sin 15°
− cos sin
− sin sin
3. cos 75° cos 25° + sin 75° sin 25°
4. cos cos
5. sin 75° cos 15° + cos 75° sin 15°
6. cos
7. cos 75° cos 15° + sin 75° sin 15°
8. sin 2 cos
9. sin 3 cos 2 − cos 3 sin 2
10. cos 2 cos + sin 2 sin
cos
Find the EXACT VALUE of each expression. Work must be shown. NO calculator!
11. sin 75°
12. cos 15°
Why are #11 and #12 the same?
13. cos(−15°)
14. sin 345°
15. cos 105°
16. sin
− sin sin
− sin
sin
− cos 2 sin
Simplify the expression. NO calculator!
17. sin(30° + ) + sin(30° − )
18. cos
+
+ cos
−
Draw and label a picture of each angle in the correct quadrant to evaluate. Calculator allowed, but NO decimal answers. Work MUST be shown.
19. GIVEN:
tan α =
and
cot =
FIND:
and is an acute positive angle
( − )
21. GIVEN:
sec α =
and
csc =
FIND:
is in the II quadrant
π<
and
<
( + )
23. Simplify:
(
)
(
cos =
FIND:
and
( − )
22. GIVEN:
tan α =
and
< 2π
<
20. GIVEN:
sin α =
and
<
<π
<
<
π<
cos =
FIND:
and 0 <
( + )
25. cos
+
)
PROVE the given equation is an identity.
24. sin( + ) = − sin
= − sin
< 2π
<π