Download Review of Chapter 5

Pre-Calculus/Trigonometry 3
Chapter 5 Review
Name __________________________________
Reciprocal Identities:
1
sin  
csc 
csc  
1
sin 
Quotient Identities:
sin 
tan  
cos 
cot  
cos  
1
sec 
tan  
1
cot 
sec  
1
cos 
cot  
1
tan 
cos 
sin 
Pythagorean Identities:
1. sin 2   cos 2   1
2. tan 2   1  sec2 
3. 1  cot 2   csc2 
Sum/Difference Identities:
sin      sin  cos   cos sin 
cos     cos cos   sin  sin 
tan     
tan   tan 
, tan  tan   1
1  tan  tan 
Double Angle Identities:
sin 2  2 sin  cos
2 tan 
tan 2 
, tan   1
1  tan 2 
cos 2  cos 2   sin 2 
cos 2  2 cos 2   1
cos 2  1  2 sin 2 
½ Angle Identities:
1
1  cos 
sin   
2
2
1
1  cos 
tan   
, cos   1
2
1  cos 
1
1  cos 
cos   
2
2
1
1  cos 
tan  
, sin   0
2
sin 
1
sin 
tan  
; cos   1
2
1  cos 
Verify each identity.
1. sec4  - tan4  = 2tan2  + 1
3.
2.
sec  tan 

1
cos  cot 
csc   sec 
 cot   1
sec 
4. sin  - 1 = tan  (cos  - cot  )
Solve each equation.
1. 4(1-cos2x) = 1
2. 5cos2x + cosx + 2 = 3cos2x + 3
3. tan 2 x  sin 2 x  cos 2 x
4. 2 sin 2 x  1  
5. 1 – cos2x + 2sin x = -1
6. sin 2  cos  0
7. cos  cos 2  0
8. Solve with a calculator: cos 2  
Find the exact value of each of the following:
9. cos(15 )
11. sin(74 ) cos(29 )  cos(74 )sin(29 )
10. tan(285 )
3
csc x
1
16