Practice with Sum/Difference and
Double and Half Angles
Chapter 5 Assign: 14
Using sum or difference formulas find each below
# 5π &
(
$ 12 '
#11π &
(
$ 12 '
1. cos%
3. tan (285)
2. sin%
4. cos( 75)
Express each as a trig function of one angle
6. cos48˚cos23˚ - sin48˚sin23˚
7. sin48˚cos23˚ - sin23˚cos48˚
€
€
€
€
13
Given csc( a ) = −
and cot (β ) = 4 / 3 and both a and β are in Q III, find
12
8. sin ( a + β )
9. tan ( a + β )
10. In which specific quadrant is a + β ?
€
€
€
Verify
€
€
11. sin ( a + π) = −sin a
€
#θ &
$2'
$
%
12. cos&θ +
π'
) = −sin
€ θ
2(
#θ &
$2'
13. 4 sin% ( cos% ( = 2 sin (θ )
€
€
4
For #14 and 15, given cot (θ ) = and the fact that θ is in QIII
3
€
14. Find sin (2θ ) , cos(2θ ) , tan (2θ )
€
€
€
Find using half angle formulas:
16. sin(15˚)
17. cos(165˚)
€
€
#θ &
$2'
#θ &
$2'
#θ &
$2'
15. Find sin% ( , cos% ( , tan% (
18. sin(157.5˚)
€
€
€
Use power reducing formulas to rewrite #19, #20 so that all terms are first degree.
3
4
19. sin (θ )
20. cos (θ )
Solve #21-26 on [0,2π )
€
21. sin (2t ) + sin ( t ) = 0
sin
23. 2€
€
22. cos( t ) − sin (2t ) = 0
€
2
(
2
25. 4 sec (θ ) −1 = 0
)
24. cos(2x ) • 2 cos( x ) + 1 = 0
(2x) = 1
€
€
€
€
€
25. 2 cos( 3x ) −1 = 0
# 7π &
(
$ 12 '
5. sin%