Name__________________________________________________________________
A2T Solving Trig Equations and Angle Formula Review
1. If x is an acute angle and sin x =
2. If sin x =
3
, then what is cos2x equal?
5
12
4
and cos y = , and x and y are acute angles, what is the value of
13
5
sin(x –y)?
3. If  is an acute angle such that sin  =
3
, what is the value of sin 2?
5
4. The expression cos 20o cos 15o + sin 20o sin 15o is equivalent to
a. cos 35o
b) sin 5o
c) cos 5o
d) sin 35o
5. Write an equation of a circle with a center of (4, -5) and a radius of 9.
6. If A and B are positive acute angles, sin A =
of sin (A + B)?
7. Show that sin 120 =
3
by using sin2(60).
2
8. Find the exact value of cos 15.
9. Solve for  in the interval 0≤≤360:
sec  + 6 = 2 sec 
10. Solve for  in the interval 0≤≤360:
cos2  - 4cos - 5 = 0
4
4
and cos B = , what is the value
7
5
11. Solve for  in the interval 0≤≤360:
1
2sin  + 1 =
sin 
12. Solve for  in the interval 0≤≤360:
3cos - 2 = 2 – cos 
13.
14.
15. Describe the roots of x2 – 2x – 15 = 0
16. The pendulum of a clock swings through an angle of 63o as it travels through an arc
of 44 centimeters. Find the length of the pendulum in centimeters.
Answer Key
1. cos 2x = 1 – 2sin2x
cos 2x = 1 – 2(3/5)2
cos 2x = 1 – 2 (9/25)
cos 2x = 1 – 18/25
cos 2x = 7/25
2. sin(x –y) = sinx cosy – cosx siny
sin(x – y) = (12/13)(4/5) – (5/13)(3/5)
sin(x – y) = 48/65 – 15/65
sin(x-y) = 33/65
3. sin2 = 2sin cos
sin2 = 2(3/5)(4/5)
sin2 = 24/25
4. c) cos 5o
5. (x – 4)2 + (y + 5)2 = 81
6. sin (A + B) = sinA cos B + cosA sinB
 33 
 (3/5)
sin(A + B ) = (4/7)(4/5) + 

7


 16   3 33  16 3 33
sin (A + B) =   + 
=
35
 35   35 
7. sin2A = 2sinAcosA
sin2(60) = 2sin60cos60
 3  1 
 
sin2(60) = 2 
 2 
2


sin2(60) =
3
2
8. cos (A-B) = cosAcosB + sinAsinB
cos (45-30) = cos45cos30 + sin45sin30
 2
3  2 1
 
cos (45-30) = 
*
* 
2   2 2 
 2
cos (15)= cos(45 -30)
6
2

4
4
6 2
cos(45 – 30) =
4
cos (45-30) =
9. {80, 280}
10. {180}
11. {30, 150, 270}
12. {0, 360}
13. {42, 138, 210, 330}
14. {90, 221.81, 318.19}
15. b2 – 4ac = 64
16. 40 cm
so the roots are real, rational and unequal