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Name:_______________________
Date:__________________
Mr. Nickels
Math 3C
Practice Trigonometric Equations Test
Part II: Show all work on a separate piece of paper.
1) Find, to the nearest tenth of a degree, all values of x in the interval 0 x <360 that
satisfy the equation 3(1-2 sin2 x) – sin x –2 = 0.
2) Find, to the nearest degree, all values of x in the interval 0  x < 360 that satisfy the
equation
2sinAcosA + cos A = 0
3) Find, to the nearest tenth of a degree, all values of x in the interval 0  x < 360 that
satisfy the equation 1-2 sin2 x – sin2 x + sin x + 1 = 0.
4) Find, to the nearest degree, all values of x in the interval 0 x <360 that satisfies the
equation 2cos2 x + cos x – 1 = 0
5) Find, to the nearest degree, all values of x in the interval 0 x <360 that satisfies the
equation 7cos x + 1 = 5cos x
Part I: Two points each.
1) Find all values of x in the interval 0 x <360 that satisfies the equation cos x = -1
2) If sin x = 3/5 express cos 2x as a fraction in simplest form.
3) Find all values of x in the interval 0 x <360 that satisfies the equation sin x = 
a. 210 and 330
b. 210
4)
1
2
c. 330
d. -30, 210 and 330
If sin A = k, then the value of the expression (sin A)(cos A)(tan A) is equivalent to
a. 1
c. k
b. 1/k
d. k2
5) Find all values of x in the interval 0 x <360 that satisfies the equation
cos x (sin x + 1) =0
6) Find the measure of the smallest positive angle that satisfies the equation
tan2 A – 3 = 0
7) 2sin 45cos 45 is equivalent to
a. sin 90
c. cos 90
b. sin 22.5
d. cos 22.5
8) Find all values of x in the interval 0 x <360 that satisfies the equation
(cos x – 1) (sin x + 1) = 0
a. 90
c. 270
b. 180
d. 360
9) Find the measure of the smallest positive angle, to nearest degree, that satisfies the
equation tan x – 2= 0
10) Find all values of x in the interval 0 x <360 that satisfies the equation
cos x = 0
11) Find all values of x, to the nearest ten minutes, in the interval 0 x <360 that satisfies
the equation
(2cos x + 1)(3sinx – 1) = 0
12) Find the number of degrees in the measure of the smallest positive angle that
satisfies the equation 2cos x + 1 = 0.
13) Find all values of x in the interval 90 x <270 that satisfies the equation
sin² x + sin x = 0
a. 90
c. 270
b. 180
d. 0
14) Find all values of x in the interval 0 x <360 that satisfies the equation
3sinx + 2 = 5
Answers:
Part II
1) 210, 330, 19.5, 160.5
4) 60, 300, 180
Part I
7
1) 180
2)
25
7) a
8) c
12) 120,
13) b
2) 90, 210, 330
5) 120, 240
3) 221.8, 318.2, 90.0
3) a
4) d
5) 90, 270
6) 60, 240
9) 63
14) 90
10) 90, 270
11) 120, 240, 19º30´, 199º30´