Free Printable PC Unit 5B Review - Solve Trig Equations

1.

Solve equation on $0\le\theta<2\pi$

$-2+\cot\theta=-3$

a)

$\theta=\frac{3\pi}{4},\frac{4\pi}{3},\frac{7\pi}{4}$

b)

$\theta=\frac{3\pi}{4},\frac{7\pi}{4}$

c)

$\theta=\frac{\pi}{3},\frac{4\pi}{3}$

d)

$\theta=\frac{3\pi}{4},\frac{4\pi}{3}$

2.

Solve equation on $0\le\theta<2\pi$ .

$1=5-8\cos\theta$

a)

$\theta=\frac{\pi}{6},\frac{\pi}{3},\frac{11\pi}{6}$

b)

$\theta=\frac{\pi}{6},\frac{11\pi}{6}$

c)

$\theta=\frac{\pi}{6}$

d)

$\theta=\frac{\pi}{3},\frac{5\pi}{3}$

3.

Solve on [0, 2π)

$4\sin^2x=3$

a)

π/6, 11π/6

b)

π/3, 2π/3

c)

π/6, 5π/6, 7π/6, 11π/6

d)

π/3, 2π/3, 4π/3, 5π/3

4.

Which of these is equivalent to 2cos²x − 3cosx = 0 ?

a)

-cos²x = 0

b)

cosx(2cosx + 3) = 0

c)

cosx(2cosx − 3) = 0

d)

cos x = ⅔

5.

Solve equation on $0\le\theta<2\pi$ .

$3\sin^2\theta+4=5+\sin^2\theta$

a)

$\theta=\frac{\pi}{4},\frac{5\pi}{4},\frac{7\pi}{4}$

b)

$\theta=\frac{\pi}{4},\frac{7\pi}{4}$

c)

$\theta=\frac{\pi}{4},\frac{3\pi}{4}$

d)

$\theta=\frac{\pi}{4},\frac{3\pi}{4},\frac{5\pi}{4},\frac{7\pi}{4}$

6.

To solve this equation, cos²x + sinx = 1, replace cos²x with

a)

1/(sec²x)

b)

sin²x − 1

c)

1 − sin²x

d)

1 + tan²x

7.

Solve on the domain [0, 2π)
cos² x + sin x + 1 = 0

a)

π

b)

3π/2

c)

π/6, 5π/6, 3π/2

d)

No solution

8.

Solve equation for $0\le\theta<2\pi$ .
$1+\tan^2\theta=4\tan^2\theta$

a)

$\theta=\frac{\pi}{6},\frac{5\pi}{6},\frac{7\pi}{6},\frac{11\pi}{6}$

b)

$\theta=\frac{\pi}{3},\frac{2\pi}{3},\frac{4\pi}{3},\frac{5\pi}{3}$

c)

$\theta=\frac{\pi}{6},\frac{7\pi}{6}$

d)

$\theta=\frac{\pi}{6},\frac{5\pi}{6},\frac{7\pi}{6}$

9.

Solve equation for $0\le\theta<2\pi$ .
$-\sin\theta\csc\theta+3\csc\theta=\sqrt{2}\sin\theta+3\csc\theta$

a)

$\theta=\frac{5\pi}{4},\frac{11\pi}{6}$

b)

$\theta=\frac{3\pi}{4},\frac{7\pi}{6},\frac{7\pi}{4}$

c)

$\theta=0,\pi,\frac{5\pi}{4},\frac{7\pi}{4}$

d)

$\theta=\frac{5\pi}{4},\frac{7\pi}{4}$

10.

Solve: 2cos(2x)= -√2

a)

$\frac{3\pi}{8},\frac{5\pi}{8},\frac{11\pi}{8},\frac{13\pi}{8}$

b)

$\frac{3\pi}{4},\frac{5\pi}{4}$

c)

$\frac{\pi}{8},\frac{7\pi}{8},\frac{9\pi}{8},\frac{15\pi}{8}$

d)

$\frac{\pi}{4},\frac{7\pi}{4}$

11.

Solve for the unknown variable on the interval 0≤x<2π

sinx + 2sinxcosx = 0

a)

2π/3, 4π/3, 0, π

b)

2π/3, 4π/3

c)

0, π

d)

π/3, 5π/3

PC Unit 5B Review - Solve Trig Equations

Total questions: 11

Worksheet time: 10mins

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