Download Use the power-reducing identities to rewrite the expression that

Use the power-reducing identities to rewrite the expression that does not contain trigonometric
functions of power greater than 1.
sin x (2 cos2 x - 1)
= sinxcos2x
Find the exact value of the product.
cos 135° cos 45°
=
1
2
Use sum-to-product identities to rewrite the expression as a product.
cos pi/11 - cos pi/8
cos

11
 cos

8

 2sin 11
 2sin

2


8 sin 11


8
2
19
3
sin
176
176
Use the information given about the angle ?, to find the exact value of the indicated trigonometric
function.
cos ? = - 5/13, ? in quadrant II Find cos 2?.
cos   
5
13
cos 2  2 cos 2   1  2 
25
119
1  
169
169
Use the information given about the angle ?, to find the exact value of the indicated trigonometric
function.
tan ? =7/24 , ? in quadrant III Find sin 2?.
tan  
7
7
24
 sin  
and cos  
24
25
25
sin 2  2sin  cos   2 
7 24 336


25 25 625
Use the product-to-sum identities to rewrite the expression as the sum or difference of two functions.
sin 6? sin 2?
sin 6 sin 2  0.5(cos8  cos 4 )
Use half-angle identities to find the exact value of the expression.
sec ( - 3pi/8)
 3
sec  
 8
1
1
1



 2.6131

 cos   3  cos  3  2cos 2  3   1


 
 
 8 
 8 
 16 
Use the information given about the angle ? to find the exact value of the indicated trigonometric
function.
csc ? = -square root 6, cos ? > 0 Find sin 0/2
cos ec   6  sin   
1
5
tan   
tan  
2 tan

2 tan

2  1 
2

5 1  tan 2 
1  tan 2
2
2
Or, tan 2
Or, tan
1
1
5
 cos   1  
6
6
6

2

2
 2 5 tan


2
1  0
2 5  20  4
 5 6
2
We will have to consider –ve value as θ is –ve.
Hence, tan
Hence, sin

2

2
 5 6

5 6
12  2 30
 0.20872
Use a double-angle identity to find the exact value of the expression.
2 tan 15 degrees/ 1- tan^(second power) 15 degree
We have tan  
2 tan
1  tan

2 .
2

2
Putting θ = 30, we get
tan 30 
Or,
2 tan15
1  tan 2 15
2 tan15
1
 tan 30 
2
1  tan 15
3