Download hw sum diff ident

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Math Analysis
Homework: Sum and Difference Identities
Evaluate the following.
1.
sin 195° using 195 = 225 – 30
3.
 17 
cos 

 12 
5.
2.
using 17  7  
12
6
tan (–105°)
 19 
sin 

 12 
4.
4
tan (–195°) using –195 = –225 +30
using –105 = –60 – 45
using
19
4



12
3
4
 
 
cos 


3 
 6
6.
Write the expression as sin, cos, or tan of an angle.
7. cos60 cos10  sin 60 sin10
8.
tan325  tan86
1  tan325 tan86
9. sin 3.5cos 1.2  cos 3.5sin 1.2
Find the exact value.
10.
Find cos(x + y) if sin x 
5

for 0  x 
13
2
11.
Find sin (x – y) if sin x 
15

for
 x
17
2
12.
Find tan(x + y) if csc x 
13

for 0  x 
5
2
& cos y 
& cot y 
4
5
24
7
& tan y 
3
4
for 0  y 
for   y 
for 0  y 

2
3
2

2
Verify the following. Show all your steps.
13.
15.
cos (π + θ) = –cos θ
cos (x + y) + cos (x – y) = 2cosxcosy
17. sin  3  x   sin x
14. tan (90°+ θ) = –cot θ
16. sin  x  y  sin( x  y )  sin x  sin y
2
18. tan  x  
  tan    x   2tan x
2