Free Printable Quarter 4 Summative Test (Trigonometry)

1.

Find the least positive coterminal angle to $-1140\degree$

a)

$60\degree$

b)

$300\degree$

c)

$420\degree$

d)

$-780\degree$

2.

What quadrant contains the terminal side of the angle $\frac{10\pi}{3}?$

a)

I

b)

II

c)

III

d)

IV

3.

Find the angle that is supplementary to $179\degree$

a)

$-179\degree$

b)

$180\degree$

c)

$181\degree$

d)

$1\degree$

4.

Find the angle complementary to $\frac{\pi}{12}$

a)

$-\frac{\pi}{12}$

b)

$-\frac{5\pi}{12}$

c)

$\frac{5\pi}{12}$

d)

$\frac{11\pi}{12}$

5.

What quadrant contains the terminal side of the angle $420\degree$ ?

a)

I

b)

II

c)

III

d)

IV

6.

Given a right triangle where $\sin\theta=\frac{3}{5}$ , find the missing side.

a)

3

b)

$\sqrt{8}$

c)

4

d)

$\sqrt{34}$

7.

Find the value of x to the nearest tenth.

a)

12.3

b)

9.1

c)

6.5

d)

8.6

8.

In the triangle below, a=22, b=17, and c=15. Find the measure of ∠A to the nearest tenth.

a)

$50.5\degree$

b)

$90.0\degree$

c)

$86.6\degree$

d)

There is not enough information.

9.

What point corresponds to the angle −π on the unit circle?

a)

(−1,0)

b)

(1,1)

c)

(1,0)

d)

(−1,−1)

e)

(0,0)

10.

Which of the following points is NOT on the unit circle?

a)

$\left(\frac{\sqrt{3}}{2},\frac{\sqrt{2}}{2}\right)$

b)

(0,−1)

c)

(1,0)

d)

$\left(-\frac{\sqrt{2}}{2},\frac{\sqrt{2}}{2}\right)$

e)

$\left(-\frac{1}{2},-\frac{\sqrt{3}}{2}\right)$

11.

When looking at the unit circle, what are the coordinates for an angle of $\frac{\pi}{4}$ ?

a)

$\left(\sqrt{2},\sqrt{2}\right)$

b)

$\left(\frac{1}{2},\frac{\sqrt{3}}{2}\right)$

c)

$\left(\frac{\sqrt{2}}{2},\frac{\sqrt{2}}{2}\right)$

d)

$\left(\frac{\sqrt{3}}{2},\frac{1}{2}\right)$

e)

(0,1)

12.

A 15foot plank has one end on the ground and one and 6feet off the ground. What is the measure of the angle formed by the plank and the ground?

a)

$≈10\degree$

b)

$≈24\degree$

c)

$≈50\degree$

d)

$≈70\degree$

13.

If the hypotenuse of a right triangle has a length of 6, and the length of a leg is 2, what is the angle between the hypotenuse and the leg?

a)

$13.54\degree$

b)

$32.12\degree$

c)

$19.47\degree$

d)

$70.53\degree$

e)

$4.87\degree$

14.

A skateboard ramp made so that the rider can gain sufficient speed before a jump is 15 feet high and the ramp is 17 feet long. What is the measure of the angle θ between the ramp and the ground?

a)

$\theta=62\degree$

b)

$\theta=20\degree$

c)

$\theta=34.2\degree$

d)

$\theta=70.4\degree$

e)

None of the other answers.

15.

Given a right triangle where $\sin\theta=\frac{3}{5}$ , find the missing side.

a)

3

b)

$\sqrt{8}$

c)

4

d)

$\sqrt{34}$

e)

$\sqrt{41}$

16.

Given a right triangle where $\tan\theta=\frac{17}{18}$

, find the missing side.

a)

17.01

b)

5.92

c)

5.29

d)

24.67

e)

24.76

17.

Given the accompanying triangle where b=6 and $\theta=17\degree$

, determine the length of the hypotenuse.

a)

1.83

b)

5.74

c)

20.52

d)

19.63

e)

1.75

18.

Given the accompanying right triangle where a=35 and c=70, determine the measure of θ to the nearest degree.

a)

$45\degree$

b)

$37\degree$

c)

$60\degree$

d)

$62\degree$

e)

$30\degree$

19.

All the squares are equal, and there are 6 squares in the figure. What is the value of $\frac{\tan\ x}{\cot\ x}$ ?

a)

$\frac{9}{4}$

b)

$\frac{2}{3}$

c)

$\frac{3}{4}$

d)

$\frac{4}{9}$

e)

$\frac{3}{2}$

20.

Find the value of x in the triangle given.

a)

16

b)

8

c)

$4\sqrt{2}$

d)

$8\sqrt{2}$

e)

$4\sqrt{3}$

21.

Choose the correct ratio.

a)

sin(37)=x/14

b)

cos(37)=x/14

c)

tan(37)=x/14

d)

sin(37)=14/x

22.

$\sin\ 24\degree=\frac{12.1}{x}$

Find the value of x.

a)

24.20

b)

290.4

c)

4.92

d)

29.75

23.

Which scenario describes the picture shown?

a)

A 5 foot ramp is 8 feet away from a building. What is the angle that the ramp makes with the ground?

b)

An 8 foot ramp leans against a building 5 feet away. What angle does the ramp make with the ground?

c)

A 5 foot ramp leans against an 8 foot structure. What is the angle that the ramp makes with the ground?

d)

A 5 foot man is 8 feet away from a building. What is the angle of elevation?

24.

Find angle B.

a)

A

b)

B

c)

C

d)

D

25.

What is the length of side x?

a)

6.57 cm

b)

7.44 cm

c)

7 cm

d)

26.33 cm

26.

Name the smallest angle in this triangle.

a)

A

b)

B

c)

C

d)

Not enough given

27.

What is the ratio for Sine?

a)

$\frac{hypotenuse\ }{opposite}$

b)

$\frac{opposite}{adjacent}$

c)

$\frac{opposite}{hypotenuse}$

d)

$\frac{adjacent\ }{opposite}$

28.

What is the ratio for tangent?

a)

$\frac{hypotenuse\ }{opposite}$

b)

$\frac{opposite}{adjacent}$

c)

$\frac{opposite}{hypotenuse}$

d)

$\frac{adjacent\ }{opposite}$

29.

What is the ratio for cosine?

a)

$\frac{hypotenuse\ }{opposite}$

b)

$\frac{opposite}{adjacent}$

c)

$\frac{opposite}{hypotenuse}$

d)

$\frac{adjacent\ }{hypotenuse}$

30.

What is the correct ratio?

a)

5/3

b)

3/4

c)

3/5

d)

4/3

31.

Which ratio represents the cos(θ)?

a)

x/y

b)

y/x

c)

x/z

d)

y/z

32.

Find the value of tan(X).

a)

3/4

b)

5/3

c)

4/3

d)

3/5

33.

Which triangle below shows the ratio as $\sin x=\frac{b}{c}$

a)

b)

c)

34.

Which triangle below shows the ratio as $\sin x=\frac{a}{c}$

a)

b)

c)

35.

Which triangle below shows the ratio as $\cos x=\frac{a}{b}$

a)

b)

c)

36.

Which triangle below shows the ratio as $\tan x=\frac{c}{a}$

a)

b)

c)

37.

Select all that apply:

What is true in respect to the relationship of the sine and cosine of complementary angles? A and B are the acute angles of the right triangle.

a)

$\sin A=\cos B$

b)

$\sin B=\cos B$

c)

$\tan A=\tan B$

d)

$\sin A=\sin A$

e)

$\sin B=\cos A$

38.

$\sin30\degree=?$

a)

$\frac{1}{2}$

b)

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

c)

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

d)

$\sqrt{3}$

39.

$\cos60\degree=?$

a)

$\frac{1}{2}$

b)

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

c)

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

d)

$\sqrt{3}$

40.

$\sin60\degree=?$

a)

$\frac{1}{2}$

b)

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

c)

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

d)

$\sqrt{3}$

Quarter 4 Summative Test (Trigonometry)

Total questions: 40

Worksheet time: 2hrs 8mins

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