Download Review 1.4 1.5 5.1-5.4

TRIGONOMETRY
REVIEW 1.4, 1.5, 5.1-5.4
NAME: _______________________________
Use sum and difference identities to find an exact value for each of the following.
1.
sin ( 75°)
4. sin 40°cos50° + cos 40°sin50°
2.
cos15o
⎛ 11π ⎞
sin ⎜
⎟
⎝ 12 ⎠
3.
5. cos 20° cos 40° − sin 20° sin 40°
6. sin
5π
π
5π
π
cos + cos sin
12
4
12
4
Solve each problem below.
7. Find the six trig function values of an angle β if sin β = −
9
40
and cos β =
.
41
41
9
41
40
cos β =
41
sin β = −
tan β =
8. Find the six trig function values of an angle γ if csc γ = −
csc β =
sec β =
cot β =
9
and γ is in quadrant III.
7
sin γ =
csc γ = −
cos γ =
sec γ =
tan γ =
cot γ =
9
7
9. Given: cos a = −
space for triangles:
60
and a is in quadrant II
61
sin b =
a) sin(a + b) ,
b) cos(a + b)
d) sin(a − b)
e)
10. Given: cos a =
space for triangles:
a)
sin(a − b)
7
and b is in quadrant I. Find
25
c) tan ( a + b ).
cos( a − b)
2
and a is in quadrant IV
3
sin b =
e) tan( a − b )
9
and b is in quadrant II. Find
41
b) cos( a − b)
Prove the following Identities
11. cos(360° − θ ) = cosθ
13.
cos( x + y )
= cot x − tan y
sin x cos y
12. cot θ + tan θ = cscθ secθ
14. cot θ tan θ + tan 2 θ = sec 2 θ
STUDY YOUR RECIPROCAL, QUOTIENT and PYTHAGOREAN ANGLE IDENTITIES
and THE UNIT CIRCLE