Free Printable Pre-Calc ECA Review

1.

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

a)

I

b)

II

c)

III

d)

IV

e)

Quadrantal Angle

2.

$\frac{19\pi}{12}$

a)

I

b)

II

c)

III

d)

IV

e)

Quadrantal Angle

3.

$-\frac{\pi}{3}$

a)

I

b)

II

c)

III

d)

IV

e)

Quadrantal Angle

4.

What is $225\degree$ in radians?

a)

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

b)

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

c)

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

d)

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

5.

What is $\frac{11\pi}{6}$ radians in degrees?

a)

30

b)

330

c)

360

d)

300

6.

Find a coterminal angle to 45 degrees.

a)

360

b)

405

c)

315

d)

295

7.

Which of the following is a negative coterminal angle of 165 degrees?

a)

-165

b)

525

c)

-525

d)

-555

8.

What are the negative and positive coterminal angles of 240 degrees?

a)

540°, -120°

b)

600°, -120°

c)

425°, -240°

d)

120°, -135°

9.

Find the arc length. Leave your answer in terms of π.

a)

7/4π

b)

7/2π

c)

1/8π

d)

45π

10.

What is the cosine of $-\frac{\pi}{3}$ radians

a)

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

b)

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

c)

$\frac{1}{2}$

d)

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

11.

What is the sine of $8\pi$ radians

a)

0

b)

1

c)

$2\pi$

d)

360

12.

What is the sine of $-\frac{3\pi}{2}$

a)

0

b)

1

c)

$\frac{\pi}{2}$

d)

$\frac{1}{2}$

13.

tan (π/6)

a)

-√3

b)

2

c)

-1 / 2

d)

√3 / 3

14.

csc π

a)

-1

b)

0

c)

1

d)

Undefined

15.

sec (2π/3)

a)

√2

b)

√3 / 3

c)

-2

d)

√3

16.

$If\ \cos\theta<0\ and\ \tan\theta<0,\$ $in\ which\ quadrant\ does\ \theta\ lies?$

a)

Quadrant I

b)

Quadrant II

c)

Quadrant III

d)

Quadrant IV

17.

Given that tanx = -5/4 and cosx > 0, what quadrant does the angle lie in?

a)

1

b)

2

c)

3

d)

4

18.

If K (5, -12) is a point on the terminal side of $\theta,$ find the exact value of sin $\theta.$

a)

$-\frac{12}{13}$

b)

$\frac{12}{13}$

c)

$\frac{5}{13}$

d)

$-\frac{12}{5}$

19.

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)

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

20.

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)

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

21.

Solve equation for $0\le\theta<2\pi$ .
$-2=-5+3\sec\theta$

a)

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

b)

$\theta=0$

c)

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

d)

$No\ Solution$

22.

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)

$\theta=0,\pi$

23.

Evaluate: cos^-1(√3/2)

a)

π/3

b)

2π/3

c)

π/6

d)

5π/6

24.

Evaluate: Csc^-1(-√2)

a)

π/4

b)

3π/4

c)

-π/4

d)

-3π/4

25.

tan(sin^-1(-1/2))

a)

√3

b)

√3/3

c)

-√3

d)

-√3/3

26.

sec^-1(-2)

a)

π/3

b)

2π/3

c)

π/6

d)

5π/6

27.

what is the amplitude of

y = -3sin (7x) -2

a)

7

b)

-2

c)

3

d)

-3

28.

What is the equation of the graph?

a)

y = 2 cos x

b)

y = sin x

c)

y = 2 sin x

d)

y = sin 2x

29.

What is the vertical shift for

y = 4 cos(x) - 2?

a)

up 2

b)

left 2

c)

right 2

d)

down 2

30.

Which is an equation of the cosine function with an amplitude of 2, period of Π, phase shift of Π/2?

a)

y= -2cos(x/2 - ∏/4)

b)

y= 2cos (x/2 + ∏)

c)

y= 2cos (2x-∏)

d)

y= -2cos(2x-∏/2)

31.

A 10 ft. tree creates a shadow that is 15 ft. long. Find the angle of elevation of the sun.

a)

34 degrees

b)

56 degrees

c)

72 degrees

d)

15 degrees

32.

A hawk sitting on a tree branch spots a mouse on the ground 15 feet from the base of the tree. The hawk swoops down toward the mouse at an angle of 30 degrees. What is the distance from the tree branch to the mouse?

a)

7.5 ft

b)

15 ft

c)

26 ft

d)

30 ft

33.

Find the length of side AB.

a)

10

b)

8

c)

6.1

d)

4.9

34.

What is the measure of angle A?

a)

58 degrees

b)

61 degrees

c)

78 degrees

d)

74 degrees

35.

Use the Law of Cosines to find the value of x. (Level 1)

a)

41.7

b)

51.7

c)

61.7

d)

71.7

36.

What is the measure of angle A?

a)

50 degrees

b)

60 degrees

c)

78 degrees

d)

74 degrees

37.

What is the length of side x?

a)

130 cm

b)

112 cm

c)

150 cm

d)

105 cm

38.

Solve the Triangle
a=38, b= 31, c= 35
Find A, B and C

a)

A= 43°, B= 47°, C= 90°

b)

A= 70°, B= 50.1°, C= 59.9°

c)

A= 50.1°, B= 70°, C= 59.9°

d)

A= 60°, B= 70°, C= 50°

39.

Find the area of $\Delta ABC$
if a = 9cm, b = 11cm, c = 16cm

a)

52.1 sq cm

b)

89.5 sq cm

c)

47.6 sq cm

d)

15.2 sq cm

40.

Find Area of ABC

a)

223.6 units²

b)

73.1 units²

c)

52.7 units²

d)

3.3 units²

41.

Simplify: $\frac{1-\sin^2x}{\sec x}$

a)

$\sin^2x$

b)

$\cos^2x$

c)

$\sin^3x$

d)

$\cos^3x$

42.

Simplify: $\frac{\sin^2x+\cos^2x+\cot^2x}{1+\tan^2x}$

a)

$\cot^2x$

b)

$\tan^2x$

c)

$\csc^2x$

d)

$\sec^2x$

43.

What is the limit?

a)

Infinity

b)

20

c)

DNE

d)

12

44.

a)

Does not exist

b)

6

c)

4

d)

3

45.

What is the limit?

a)

DNE

b)

Infinity

c)

6

d)

12

46.

a)

-7

b)

0

c)

1

d)

DNE

47.

a)

A

b)

B

c)

C

d)

D

Pre-Calc ECA Review

Total questions: 47

Worksheet time: 2hrs 58mins

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