Pre-Calculus 12:
1.
Worksheet #6
Chapter 7
Write each expression in terms of a single trigonometric function.
a) 2 sin 0.6 cos 0.6
b) 2 sin 3 cos 3
c) 2sin2cos2
d) cos 2 0.45  sin 2 0.45
e) 2 cos 2 5  1
f) 1  2 sin 2 3
2.
Write each expression in terms of a single trigonometric function
a) 2 sin
b) cos 2

6
cos

10

6
 sin 2

10
c) 2 cos 2 0.5  1
3.
If sin  
a) sin 2
1
and  is in quadrant I, evaluate each expression.
3
b) cos 2
c) tan 2
4.
A value of  is defined. Evaluate the expressions sin 2 , cos 2 , and tan 2
1
a) cos    , and  is in Quadrant II
2
2
b) sin    , and  is in Quadrant III
3
c) tan  0.75 and    
5.
3
2
Prove each identity:
2
a) 1  sin 2  sin   cos  
b) sin 2  2 cot  sin 2 
1  tan 2 
c) cos 2 
1  tan 2 
d) sec 2  
6.
2
1  cos 2
Prove each identity:
1  cos 2
 sin 2 
a)
2
sin 2   cos 2 
b)
  sec 2
sin 2   cos 2 
c)
sin   cos  2
sin 2
 csc 2  1
Answers:
1a) sin 1.2
b) sin 6
c) sin 4
2a) sin
b) cos
c) cos 1


3
5
4 2
7
3a)
b)
9
9
3
1
,  , 3
4a) 
2
2
d) cos 0.9
4 2
7
4 5 1
, , 4 5
b)
9
9
e) cos 10
f) cos 6
c)
c)
24 7 24
,
,
25 25 7