HW 9-5 Double and Half Angle Identities
Name ____________________________________
Use the identities on your gold formula sheet to help you answer each question below. As is often the case,
drawing a reference triangle will make this process much easier. Leave all answers in fractional form.
1
If sin  
 3
and  terminates in quadrant III, express each value below:
2
a) sin 2 
b) cos 2 
2
Solve algebraically for x, such that 0  x  360 .
a) cos 2x  cos x  0
b) cos 2x  1  2 sin x
c) sin 2x  cos x  0
 12
3
and  terminates in quadrant II; sin  
and  terminates in quadrant III.
5
13
Express each value below:
Given: sin  
3
a) sin(    ) 
b) cos(   ) 
c) sin(    ) 
d) cos(   ) 
4
Write each expression as a monomial containing a single fraction or a constant.
a)
sec  (1  sin 2  )
b)
sec cot  sin 
c)
tan  (cot   tan  )
5
Solve for  such that 0    360 . Round answers to nearest minute, if necessary.
2 sec 2   3 tan   1