Free Printable Unit 6 Quiz Review

1.

Solve equation for $0\le\theta<2\pi$ .
$1=5-8\cos\theta$

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)

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

2.

Solve equation for $0\le\theta<2\pi$ .
$-2+\cot\theta=-3$

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)

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

3.

Solve\ \ \ 4\cos x+3=5\ \ \ for\ 0\le x<360\degree

a)

$x\ =\ 60\degree,\ 120\degree$

b)

$x\ =\ 60\degree,\ 300\degree$

c)

$x\ =\ 30\degree,\ 150\degree$

d)

$x\ =\ 30\degree,\ 330\degree$

4.

$Solve\ \ \tan\ x\ +\ \sqrt{3}\ =\ 0\ \ for\ 0\ \le\ x\ <\ 360\degree$

a)

$30\degree,\ 210\degree$

b)

$150\degree,\ 330\degree$

c)

$60\degree,\ 240\degree$

d)

$120\degree,\ 300\degree$

5.

Solve equation for $0\le\theta<2\pi$ .
$-1-2\sec^2\theta=-3\sec^2\theta$

a)

$\theta=0,\pi,\frac{4\pi}{3}$

b)

$\theta=0$

c)

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

d)

$\theta=0,\pi$

6.

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)

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

7.

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

a)

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

b)

$\theta=0,\frac{5\pi}{6},\pi,\frac{11\pi}{6}$

c)

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

d)

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

8.

Solve the equation. Restrict your answer to [0,2π).

$-2\sqrt{2}=4\sin3\theta$

a)

$\left\{\frac{\pi}{24},\frac{13\pi}{24},\frac{7\pi}{12},\frac{25\pi}{24},\frac{29\pi}{24},\frac{5\pi}{4},\frac{7\pi}{4}\right\}$

b)

$\left\{\frac{7\pi}{12},\frac{25\pi}{24},\frac{13\pi}{12},\frac{7\pi}{4},\frac{23\pi}{12}\right\}$

c)

$\left\{\frac{25\pi}{24},\frac{41\pi}{24},\frac{7\pi}{4}\right\}$

d)

$\left\{\frac{5\pi}{12},\frac{7\pi}{12},\frac{13\pi}{12},\frac{5\pi}{4},\frac{7\pi}{4},\frac{23\pi}{12}\right\}$

9.

Solve the equation for solutions in the interval [0°, 360°)
$2\csc\theta-4=0$

a)

$\theta=\left\{-30\degree,\ 120\degree\right\}$

b)

$\theta=\left\{30°,\ 150°\right\}$

c)

$\theta=\left\{60°,\ 300°\right\}$

d)

$\theta=\left\{60°,\ 120°\right\}$

10.

Solve the equation for solutions in the interval [0°, 360°)
$2\cos^2\theta+\cos\theta-1=0$

a)

$\theta=\left\{60°,180°,300°\right\}$

b)

$\theta=\left\{30°,120°,240°\right\}$

c)

$\theta=\left\{15°,75°,135°\right\}$

d)

$\theta=\left\{60°,120°,270°\right\}$

11.

Solve the equation for solutions in the interval [0°, 360°)
$-1+\frac{1}{3}\csc\theta=-\frac{5}{3}$

a)

No Solution

b)

$\theta=\left\{210°,330\degree\right\}$

c)

$\theta=\left\{210°,270°,330°\right\}$

d)

$\theta=\left\{240°,270°\right\}$

12.

Evaluate the function: arcsin(-1/2)

a)

π/3

b)

π/6

c)

5π/6

d)

-π/6

13.

Evaluate: cos^-1(√3/2)

a)

π/3

b)

2π/3

c)

π/6

d)

5π/6

14.

Evaluate: Csc^-1(-√2)

a)

π/4

b)

3π/4

c)

-π/4

d)

-3π/4

15.

a)

A

b)

B

c)

C

d)

D

16.

a)

A

b)

B

c)

C

d)

D

17.

$\tan\ \left(\sin^{-1}\ \left(\frac{-3}{5}\right)\right)$ = ________

a)

$\frac{4}{3}$

b)

$-\frac{4}{3}$

c)

$\frac{3}{4}$

d)

$-\frac{3}{4}$

18.

Find the following without your calculator $\cot\left(\arcsin\frac{\sqrt{3}}{2}\right)$

a)

$0$

b)

$1$

c)

$\frac{\sqrt{2}}{2}$

d)

$\frac{\sqrt{3}}{3}$

Unit 6 Quiz Review

Total questions: 18

Worksheet time: 2hrs 30mins

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