Free Printable Trig Midterm

1.

Find m<B

a)

A

b)

B

c)

C

d)

D

2.

Find the missing side.

a)

15.9 in.

b)

22.8 in.

c)

19.2 in.

d)

521.1 in.

3.

Find the area to the nearest tenth

(a)

4.

Find the area of ABC to the nearest tenth.

a)

62.3 units²

b)

124.6 units²

c)

77.0 units²

d)

100 units²

5.

Find the measure of the missing angle.

a)

64^o

b)

26^o

c)

61^o

d)

.008^o

6.

Which equation would you use to solve for the unknown angle?

a)

x =cos^–1(68/85)

b)

x = cos^–1(85/68)

c)

x = cos^–1(51/85)

d)

x = cos^–1(85/51)

7.

Match the following trig functions to the correct trig values

a)

1

1.

cos(0)

b)

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

2.

cos( $\frac{\pi}{6}$ )

c)

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

3.

cos( $\frac{\pi}{4}$ )

d)

$\frac{\ 1}{2}$

4.

cos( $\frac{\pi}{3}$ )

e)

0

5.

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

8.

Add:

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

a)

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

b)

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

c)

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

d)

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

9.

The NEGATIVE co-terminal angle for $-120\degree$ is (a) degrees.

10.

The POSITIVE co-terminal angle for $300\degree$ is (a) degrees.

11.

Find the NEGATIVE co-terminal angle for:

$\frac{\pi}{2}$

a)

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

b)

$-\frac{5\pi}{2}$

c)

$-\frac{4\pi}{4}$

d)

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

12.

Find the POSITIVE co-terminal angle for:

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

a)

$\frac{17\pi}{7}$

b)

$-\frac{11\pi}{7}$

c)

$\frac{17\pi}{14}$

d)

$\frac{5\pi}{7}$

13.

Find the length of the bold arc.

a)

54.7 mi

b)

335.1 mi

c)

16.8 mi

d)

33.5 mi

14.

Find the area of the sector.

a)

A

b)

B

c)

C

d)

D

15.

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

a)

$\frac{1}{3}$

b)

$-\frac{1}{3}$

c)

$\frac{1}{9}$

d)

$-\frac{1}{9}$

16.

Expand $\cos\ \left(\frac{\pi}{5}+\frac{\pi}{6}\right)$

a)

$\cos\frac{\pi}{5}\cos\frac{\pi}{6}-\sin\frac{\pi}{5}\sin\frac{\pi}{6}\$

b)

$\cos\frac{\pi}{5}\cos\frac{\pi}{6}+\sin\frac{\pi}{5}\sin\frac{\pi}{6}\$

c)

$\cos\ \frac{2\pi}{11}$

d)

$\cos\frac{\pi}{5}\sin\frac{\pi}{6}-\cos\frac{\pi}{5}\sin\frac{\pi}{6}\$

17.

Use a sum or difference identity to find the EXACT value:
$\sin\left(75\degree\right)$

a)

-0.3879

b)

0.9659

c)

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

d)

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

18.

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)

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

19.

Solve for x. Round to the nearest tenth.

a)

15.3

b)

16.6

c)

24.1

d)

24.3

20.

Solve for x. Round to the nearest tenth.

a)

10.4

b)

8.9

c)

31.2

d)

10.5

21.

Convert 35π / 18 radians into degrees

a)

350^o

b)

340^o

c)

355^o

d)

345⁰

22.

Convert 510^o to Radians

a)

25π / 3

b)

23π / 8

c)

17π / 6

d)

51π / 8

23.

sin 7π/6

a)

1/2

b)

-1/2

c)

√3/2

d)

-√3/2

24.

a)

√3/3

b)

√3

c)

1

d)

undefined

25.

What is the reference angle for 125°?

a)

235°

b)

125°

c)

75°

d)

55°

26.

What is the reference angle for -310⁰?

a)

50⁰

b)

-50⁰

c)

20⁰

d)

40⁰

27.

What is the period of this graph?

a)

2π

b)

π/2

c)

π/4

d)

π

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 equation of the midline of this graph?

a)

y=3

b)

x=1

c)

Impossible to find without more information

d)

y=-2

30.

Which equation best represents the graph pictured above?

a)

$y=3\sin x+1$

b)

$y=3\cos x+1$

c)

$y=2\sin x+1$

d)

$y=2\cos x+1$

31.

A tourist views a deer from a height of 45 feet. The horizontal distance between the tourist and the deer is 130 feet. How many degrees should the tourist tilt his camera down to photograph the deer? Round your answer to the nearest degree.

a)

19 degrees

b)

45 degrees

c)

71 degrees

d)

138 degrees

32.

tanθ is positive in

a)

the 1st and 2nd quadrants

b)

the 1st and 3rd quadrants

c)

the 1st and 4th quadrants

d)

the 2nd and 3rd quadrants

33.

Find the direction of the vector <-3, -5>.

a)

59.03°

b)

239.03°

c)

210.96°

d)

120.96°

34.

Find the magnitude of the vector <2, -3>.

a)

√11

b)

13

c)

√-4

d)

√13

35.

Find the unit vector in the same direction as v.

a)

<0.385, 0.923>

b)

<-0.832, 0.555>

c)

<5/13, 12/13>

d)

<-5/13, -12/13>

36.

Determine the direction and magnitude of the vector 〈7,18〉

a)

Direction 21.3°
Magnitude 19.3

b)

Direction 68.7°
Magnitude 19.3

c)

Direction 21.3°
Magnitude 373

d)

Direction 68.7°
Magnitude 373

37.

Convert to polar

a)

A

b)

B

c)

C

d)

D

38.

A vector is a ray with both ____________ and _____________.

a)

Wings and halos

b)

Space and time

c)

Direction and magnitude

d)

Radicals and exponents

39.

If vector B is <0,6>

find -5B

< (a) , (b) >

Choose from the below words

0

-30

6

-5

-1

10

1

40.

If a turtle moves from coordinate
P = (3,2) to
Q = (5,6). Which vector models the turtle's motion?

a)

〈-2,-4〉

b)

〈2,4〉

c)

〈8,8〉

d)

none of these

Trig Midterm

Total questions: 40

Worksheet time: 2hrs 11mins

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