Free Printable Chapter 6 Solving trig equations

1.

Find ALL the solutions between [0, 360 $\degree$ ) for this equation:
sin x = 1/2

a)

60 $\degree$

b)

30 $\degree$

c)

150 $\degree$

d)

330 $\degree$

e)

120 $\degree$

2.

Find all the solutions [0, 360 $\degree$ ) for this equation:
tan x = -1

a)

135 $\degree$

b)

45 $\degree$

c)

225 $\degree$

d)

180 $\degree$

e)

315 $\degree$

3.

Find all the solutions [0, 2π) for this equation:
tan x = 0 (remember 0 = $\frac{0}{\pm1}$ , so 2 possible answers)

a)

0

b)

π/2

c)

π

d)

3π/2

e)

2π

4.

Find all the solutions [0, 2π) for this equation:
2sin x + $\sqrt{3}$ = 0

a)

π/3

b)

2π/3

c)

5π/6

d)

4π/3

e)

5π/3

5.

$\sin⁡θ(2\cosθ+1)=0$
Solve the equation for the interval [0°, 360°).

a)

{90°, 150°, 210°, 270°}

b)

{0°, 120°, 180°, 240°}

c)

{0°, 60°, 120°, 180°, 240°, 300°}

d)

{0°, 180°}

6.

$2\cos^2\theta=1$
Solve the equation for the interval [0, $2\pi$ ).

a)

$\frac{π}{4},\frac{3π}{4},\frac{5π}{4},\frac{7π}{4}$

b)

$\frac{π}{6},\frac{5π}{6},\frac{7π}{6},\frac{11π}{6}$

c)

$\frac{π}{4},\frac{7π}{4}$

d)

$\frac{π}{3},\frac{5π}{3}$

7.

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

8.

Which is a correct way to solve the equation

cosx(2cosx − 3) = 0?

a)

divide cos x from both sides

b)

set each factor equal to 0 and solve

c)

distribute cosx into the parentheses

d)

guess and hope for the best

9.

Choose a good way to start solving this equation

tanx sin²x = 2 tanx

a)

divide tanx from both sides

b)

factor out tanx

c)

subtract 2 tanx from both sides and then factor tanx out

d)

cancel sin²x out

10.

Factor 0 = sin²x − sinx

a)

0 = sinx(sinx)

b)

0 = sinx(1 − sinx)

c)

0 = cosx(sinx − 1)

d)

0 = sinx(sinx − 1)

11.

Factor: sec²x − secx − 2

a)

(sec x)(secx − 2)

b)

(secx − 2)(secx − 1)

c)

(secx − 2)(secx + 1)

d)

(secx + 2)(secx − 1)

12.

Find the solution on the interval [0, 2π)

a)

0; π

b)

π; π/4; 3π/4; 5π/4; 7π/4

c)

0; π; π/4; 3π/4; 5π/4; 7π/4

d)

No Solution

13.

Find the solution over the interval [0, 2π)

a)

π/3; 5π/3

b)

π/3

c)

5π/3

d)

π/3+2πn; 5π/3+2πn

14.

Solve equation for $0\le\theta<2\pi$ .
$\sec^2\theta+3=2\sec\theta+2$

a)

$\theta=0,\frac{\pi}{2},\frac{2\pi}{3},\frac{5\pi}{3}$

b)

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

c)

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

d)

$\theta=0$

15.

Solve:

2\cos2x+3=2

a)

$x=\frac{2\pi}{3},\ \frac{4\pi}{3},\ \frac{5\pi}{3},\ \frac{7\pi}{3}$

b)

$x=\frac{\pi}{3},\frac{2\pi}{3}$

c)

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

d)

$x=\frac{2\pi}{3},\ \frac{4\pi}{3}$

16.

Solve in the interval [0, 2π):

3\tan^2\left(\frac{x}{2}\right)-9=0

a)

$x=\frac{2\pi}{3}$

b)

$x=\frac{\pi}{3};\ x=\frac{2\pi}{3};\ x=\frac{4\pi}{3};\ x=\frac{5\pi}{3}$

c)

$x=\frac{2\pi}{3};\ x=\frac{4\pi}{3}$

d)

$x=\pm2\sqrt{3}$

17.

Solve for ALL answers such that

0\le x<2\pi

:

\cos2x=\frac{\sqrt{2}}{2}

a)

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

b)

$x=\frac{\pi}{4},\frac{7\pi}{4},\frac{9\pi}{4},\frac{15\pi}{4}$

c)

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

d)

$No\ Solution$

18.

Solve for ALL answers such that

0\le x<2\pi

:

\tan3x=1

a)

$x=\frac{\pi}{12},\frac{5\pi}{12},\frac{3\pi}{4},\frac{13\pi}{12},\frac{17\pi}{12},\frac{7\pi}{4}$

b)

$x=\frac{\pi}{4},\frac{5\pi}{4},\frac{9\pi}{4},\frac{13\pi}{4},\frac{17\pi}{4},\frac{21\pi}{4}$

c)

$No\ Solutions$

d)

$x=\frac{\pi}{4},\frac{5\pi}{4}$

19.

Solve for ALL answers such that

0\le x<2\pi

:

\csc3x=-\frac{2\sqrt{3}}{3}

a)

$x=\frac{4\pi}{9},\frac{5\pi}{9},\frac{10\pi}{9},\frac{11\pi}{9}$

b)

$x=\frac{4\pi}{9},\frac{5\pi}{9},\frac{10\pi}{9},\frac{11\pi}{9},\frac{16\pi}{9},\frac{17\pi}{9}$

c)

$x=\frac{4\pi}{3},\frac{5\pi}{3},\frac{10\pi}{3},\frac{11\pi}{3},\frac{16\pi}{3},\frac{17\pi}{3}$

d)

$No\ Solutions$

20.

Solve for ALL answers such that

0\le x<2\pi

:

\frac{1}{2}=\sin3x

a)

$x=\frac{\pi}{18},\frac{5\pi}{18},\frac{13\pi}{18},\frac{17\pi}{18},\frac{25\pi}{18},\frac{29\pi}{18}$

b)

$x=\frac{\pi}{18},\frac{5\pi}{18},\frac{13\pi}{18},\frac{17\pi}{18}$

c)

$x=\frac{\pi}{6},\frac{5\pi}{6},\frac{13\pi}{6},\frac{17\pi}{6},\frac{25\pi}{6},\frac{29\pi}{6}$

d)

$x=\frac{\pi}{6},\frac{5\pi}{6}$

Chapter 6 Solving trig equations

Total questions: 20

Worksheet time: 38mins

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