Free Printable Precalculus A Unit 2 Review

1.

Nga is watching a bird flying at an altitude of 7 km. If the angle of elevation is $\frac{\pi}{6}$ then the distance between Nga and the bird is how many kilometers? [Round your answer to the nearest tenth if necessary]

(a)

2.

Match the trigonometric functions that have the same value.

a)

$\sin\left(\frac{8\pi}{13}\right)$

1.

$\sin\left(\frac{5\pi}{13}\right)$

b)

$\sin\left(\frac{7\pi}{13}\right)$

2.

$\sin\left(\frac{6\pi}{13}\right)$

c)

$\sin\left(\frac{10\pi}{13}\right)$

3.

$\sin\left(\frac{3\pi}{13}\right)$

d)

$\cos\left(\frac{5\pi}{13}\right)$

4.

$\cos\left(\frac{21\pi}{13}\right)$

e)

$\cos\left(\frac{8\pi}{13}\right)$

5.

$\cos\left(\frac{18\pi}{13}\right)$

3.

Match the angles between radians and degrees

a)

$\frac{\pi}{3}$

1.

60°

b)

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

2.

135°

c)

$\frac{7\pi}{6}$

3.

210°

d)

$\frac{\pi}{2}$

4.

90°

e)

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

5.

300°

4.

Triangle ABC has vertices A(1,2), B(6,2), and C(6,14). What is $\sin\angle CAB$ ?

a)

$\frac{12}{13}$

b)

$\frac{5}{13}$

c)

$\frac{5}{12}$

d)

$\frac{14}{6}$

5.

Triangle ABC has vertices A(1,2), B(6,2), and C(6,14). What is $\tan\angle ACB$ ?

a)

$\frac{12}{13}$

b)

$\frac{5}{13}$

c)

$\frac{5}{12}$

d)

$\frac{14}{6}$

6.

A construction worker paces the base of a ladder 3.5 meters from a building at an angle of 60°. What is the approximate height of the building?

a)

5.7 m

b)

7.0 m

c)

3.0 m

d)

6.1 m

7.

What is the approximate value of $\theta$ if $\sin\theta=\frac{14}{15}$ ?

a)

89°

b)

69°

c)

39°

d)

19°

8.

Find the value of y.

a)

$8$

b)

$4$

c)

$2\sqrt{3}$

d)

$8\sqrt{3}$

9.

Find the value of y.

a)

$9$

b)

$18\sqrt{2}$

c)

$9\sqrt{2}$

d)

$\frac{9\sqrt{2}}{2}$

10.

What type of symmetry does an even function have?

a)

reflection

b)

rotation

11.

What type of symmetry does an odd function have?

a)

reflection

b)

rotation

12.

Is tangent an even or odd function?

a)

even

b)

odd

c)

neither

13.

The product of an even and an odd function is ...

a)

an even function

b)

an odd function

c)

neither an even nor an odd function

d)

both an even and an odd function

14.

The quotient of two odd function is ...

a)

an even function

b)

an odd function

c)

neither an even nor an odd function

d)

both an even and an odd function

15.

The difference of two even functions is ...

a)

an even function

b)

an odd function

c)

neither an even nor an odd function

d)

both an even and an odd function

16.

The sum of an even function and an odd function is ...

a)

an even function

b)

an odd function

c)

neither an even nor an odd function

d)

both an even and an odd function

17.

What is the period of $y=2\cos3x$ ?

a)

$2\pi$

b)

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

c)

$\pi$

d)

$6\pi$

18.

What is the value of $\arctan\left(\frac{1}{\sqrt{3}}\right)$ ?

a)

30°

b)

60°

c)

120°

d)

150°

e)

210°

19.

$\sin^2x+\cos^2x=$

a)

$1$

b)

$\frac{1}{\sin x}$

c)

$\sec^2x$

d)

$\csc^2x$

20.

Simplify $\frac{\sec^2\theta-1}{\sec^2\theta}$

a)

$\sinθ$

b)

$\cos^2θ$

c)

$\sin^2θ$

d)

$1-\sin^2θ$

21.

Find the solutions of the equation in the interval $\left[0,2\pi\right)$

$2\cos\theta+1=0$

a)

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

b)

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

c)

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

d)

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

22.

Use a sum or difference identity to find the EXACT value:

$\sin\left(15\degree\right)$

a)

0.2588

b)

0.6503

c)

$\frac{\sqrt{6}-\sqrt{2}}{4}$

d)

$\frac{\sqrt{2}-\sqrt{6}}{4}$

23.

Use a sum or difference identity to find the EXACT value:

$\cos\left(105\degree\right)$

a)

-0.2410

b)

-0.2588

c)

$\frac{\sqrt{6}-\sqrt{2}}{4}$

d)

$\frac{\sqrt{2}-\sqrt{6}}{4}$

24.

Write the expression as the sine or cosine of a single angle:

$\sin42\degree\cos17\degree-\cos42\degree\sin17\degree$

a)

$\sin\left(59\degree\right)$

b)

$\cos\left(59\degree\right)$

c)

$\sin\left(25\degree\right)$

d)

$\cos\left(25\degree\right)$

25.

Write the expression as the sine or cosine of a single angle:

$\cos94\degree\cos18\degree+\sin94\degree\sin18\degree$

a)

$\cos\left(76\degree\right)$

b)

$\sin\left(76\degree\right)$

c)

$\cos\left(112\degree\right)$

d)

$\sin\left(112\degree\right)$

26.

$\sin\left(\frac{\pi}{2}-\theta\right)\ =\$

a)

$\cos\theta$

b)

$\frac{1}{\sec\theta}$

c)

$\frac{1}{\sec\left(\frac{\pi}{2}-\theta\right)}$

d)

$\cos\left(\frac{\pi}{2}\right)$

27.

Use a double-angle or half-angle identity to find the exact value of $\sin2θ$ , when

$\cosθ=\frac{4}{5}$ and $270°<θ<360°$

a)

$-\frac{1}{5}$

b)

$\frac{24}{25}$

c)

$-\frac{24}{25}$

d)

$-\frac{25}{24}$

28.

Use a double-angle or half-angle identity to find the exact value of $\tan\frac{\theta}{2}$ , when $\sinθ=-\frac{3}{5}$ and $\frac{3\pi}{2}<θ<2\pi$

a)

$-\frac{1}{3}$

b)

$-\sqrt{3}$

c)

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

d)

$-1$

29.

If $\cos\theta=\frac{1}{8},$ the positive value of $\sin\ \frac{\theta}{2}$ is

a)

$\frac{3}{2}$

b)

$\frac{\sqrt{7}}{4}$

c)

$\frac{9}{16}$

d)

$\frac{3}{4}$

30.

If $\sin\theta=\frac{\sqrt{5}}{3}$ , then $\cos2\theta$ equals

a)

$\frac{1}{3}$

b)

$-\frac{1}{3}$

c)

$\frac{1}{9}$

d)

$-\frac{1}{9}$

31.

Write the following product as a sum:

\cos45\degree\cos15\degree

a)

$\frac{1}{2}\left[\sin\left(60\degree\right)+\sin\left(30\degree\right)\right]$

b)

$\frac{1}{2}\left[\sin\left(60\degree\right)-\sin\left(30\degree\right)\right]$

c)

$\frac{1}{2}\left[\cos\left(60\degree\right)+\cos\left(30\degree\right)\right]$

d)

$\frac{1}{2}\left[\cos\left(30\degree\right)-\cos\left(60\degree\right)\right]$

32.

Write the following sum as a product:

$\cos2\theta-\cos8\theta$

a)

$2\sin\frac{2\theta+8\theta}{2}\cos\frac{2\theta-8\theta}{2}$

b)

$2\cos\frac{2\theta+8\theta}{2}\sin\frac{2\theta-8\theta}{2}$

c)

$2\cos\frac{2\theta+8\theta}{2}\cos\frac{2\theta-8\theta}{2}$

d)

$-2\sin\frac{2\theta+8\theta}{2}\sin\frac{2\theta-8\theta}{2}$

33.

Use the Half-Angle Identity to find the exact value of $\cos\left(\frac{5\pi}{12}\right)$

a)

$\frac{\sqrt{\sqrt{3}-2}}{2}$

b)

$\frac{\sqrt{2-\sqrt{3}}}{2}$

c)

$-\frac{\sqrt{\sqrt{3}-2}}{2}$

d)

$-\frac{\sqrt{2-\sqrt{3}}}{2}$

34.

Solve for $0\le x<2\pi$

$4\cos^2x-2=0$

a)

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

b)

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

c)

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

d)

$\frac{5\pi}{6},\ \frac{11\pi}{6}$

35.

Solve for $0\le x<2\pi$

$\sin x\tan x=\sin x$

a)

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

b)

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

c)

$0,\ \pi$

d)

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

36.

Solve for $0\le x<2\pi$

$2\sin^2x-5\sin x+2=0$

a)

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

b)

$\frac{7\pi}{6},\ \frac{11\pi}{6}$

c)

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

d)

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

37.

Select all possible answers to the equation $4\sin^2u+8=11$

a)

$\frac{\pi}{3}$

b)

$2\pi$

c)

$\frac{\pi}{6}$

d)

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

e)

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

38.

Find the solution over the interval $[0,\ 2\pi)$ of $3\tan^3x-\tan x=0$

a)

$0,\ \pi,\ \frac{\pi}{6},\ \frac{7\pi}{6}$

b)

$0,\ \frac{\pi}{6},\ \frac{7\pi}{6}$

c)

$\pi,\ \frac{5\pi}{6},\ \frac{11\pi}{6}$

d)

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

Precalculus A Unit 2 Review

Total questions: 38

Worksheet time: 1hrs 7mins

Similar Resources on Wayground