Free Printable Review and Trig Identities

1.

Convert $\frac{\pi}{3}$ radians to degrees

a)

60⁰

b)

30⁰

c)

90⁰

d)

45⁰

2.

Convert $\frac{\pi}{4}$ to degrees

a)

90⁰

b)

45⁰

c)

60⁰

d)

30⁰

3.

Convert 270^o into radians

a)

π/ 4

b)

3π/ 2

c)

3π/ 4

d)

π/ 2

4.

State which quadrant the following angle is located:

a)

Quadrant I

b)

Quadrant II

c)

Quadrant III

d)

Quadrant IV

(four)

5.

State which quadrant the following angle is located:

a)

Quadrant I

b)

Quadrant II

c)

Quadrant III

d)

Quadrant IV

(four)

6.

State which quadrant the following angle is located: $210\degree$

a)

Quadrant I

b)

Quadrant II

c)

Quadrant III

d)

Quadrant IV

(four)

7.

State which quadrant the following angle is located: $\frac{5\pi}{6}\ radians$

a)

Quadrant I

b)

Quadrant II

c)

Quadrant III

d)

Quadrant IV

(four)

8.

State which quadrant the following angle is located: $\frac{\pi}{3}\ radians$

a)

Quadrant I

b)

Quadrant II

c)

Quadrant III

d)

Quadrant IV

(four)

9.

State which quadrant the following angle is located: $\frac{7\pi}{4}\ radians$

a)

Quadrant I

b)

Quadrant II

c)

Quadrant III

d)

Quadrant IV

(four)

10.

State which quadrant the following angle is located: $\frac{2\pi}{3}\ radians$

a)

Quadrant I

b)

Quadrant II

c)

Quadrant III

d)

Quadrant IV

(four)

11.

State which quadrant the following angle is located: $\frac{11\pi}{6}\ radians$

a)

Quadrant I

b)

Quadrant II

c)

Quadrant III

d)

Quadrant IV

(four)

12.

State which quadrant the following angle is located: $\frac{5\pi}{3}\ radians$

a)

Quadrant I

b)

Quadrant II

c)

Quadrant III

d)

Quadrant IV

(four)

13.

State which quadrant the following angle is located: $\frac{3\pi}{4}\ radians$

a)

Quadrant I

b)

Quadrant II

c)

Quadrant III

d)

Quadrant IV

(four)

14.

State which quadrant the following angle is located: $\frac{4\pi}{3}\ radians$

a)

Quadrant I

b)

Quadrant II

c)

Quadrant III

d)

Quadrant IV

(four)

15.

State which quadrant the following angle is located: $-120\degree$

a)

Quadrant I

b)

Quadrant II

c)

Quadrant III

d)

Quadrant IV

(four)

16.

What is the reference angle for -30°?

a)

150°

b)

30°

c)

80°

d)

60°

17.

What is the reference angle for 240 degrees?

a)

60 degrees

b)

30 degrees

c)

45 degrees

d)

210 degrees

18.

$225\degree$ State the related reference angle

a)

$0\degree$

b)

$30\degree$

c)

$45\degree$

d)

$60\degree$

e)

$90\degree$

19.

$300\degree$ State the related reference angle

a)

$0\degree$

b)

$30\degree$

c)

$45\degree$

d)

$60\degree$

e)

$90\degree$

20.

$210\degree$ State the related reference angle

a)

$0\degree$

b)

$30\degree$

c)

$45\degree$

d)

$60\degree$

e)

$90\degree$

21.

$315\degree$ State the related reference angle

a)

$0\degree$

b)

$30\degree$

c)

$45\degree$

d)

$60\degree$

e)

$90\degree$

22.

$330\degree$ State the related reference angle

a)

$0\degree$

b)

$30\degree$

c)

$45\degree$

d)

$60\degree$

e)

$90\degree$

23.

$135\degree$ State the related reference angle

a)

$0\degree$

b)

$30\degree$

c)

$45\degree$

d)

$60\degree$

e)

$90\degree$

24.

$150\degree$ State the related reference angle

a)

$0\degree$

b)

$30\degree$

c)

$45\degree$

d)

$60\degree$

e)

$90\degree$

25.

$\sin\frac{\pi}{4}$

a)

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

b)

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

c)

1/2

d)

1

26.

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

a)

$-\frac{1}{2}$

b)

$\frac{1}{2}$

c)

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

d)

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

27.

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

a)

$-\frac{1}{2}$

b)

$\frac{1}{2}$

c)

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

d)

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

28.

$\sin\ \frac{11\pi}{6}$

a)

$-\frac{1}{2}$

b)

$\frac{1}{2}$

c)

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

d)

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

29.

\cos\ \frac{4\pi}{3}

a)

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

b)

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

c)

$\frac{1}{2}$

d)

$-\frac{1}{2}$

30.

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

a)

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

b)

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

c)

$\frac{1}{2}$

d)

$-\frac{1}{2}$

31.

What is the value of sine at 210?

a)

1/2

b)

-1/2

c)

√3 / 2

d)

-√3 / 2

32.

cos 5π/6

a)

-1/2

b)

1/2

c)

√3/2

d)

-√3/2

33.

a)

-1

b)

0

c)

undefined

d)

√3

34.

sinθ 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

35.

cosθ 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

36.

tan 7π/4

a)

-1

b)

1

c)

√2/2

d)

undefined

37.

sin 90°

a)

1

b)

0

c)

-1

d)

UD

38.

cos 270°

a)

1

b)

0

c)

-1

d)

UD

39.

Evaluate: $\sin\pi$

a)

$0$

b)

$1$

c)

$-1$

d)

undefined

40.

Evaluate: $\cot\ 270\degree$

a)

$0$

b)

$1$

c)

$-1$

d)

undefined

41.

sec 3π/2

a)

0

b)

undefined

c)

1

d)

-1

42.

sec 360^o

a)

0

b)

1

c)

-1

d)

und

43.

What is cos 90°?

a)

½

b)

undefined

c)

1

d)

0

44.

Solve the following for cos²θ:
sin²θ + cos²θ = 1

a)

cos²θ = 1 - sin²θ

b)

cosθ = 1 + sin²θ

c)

cosθ = 1 - sinθ

d)

cos²θ = Adj/hyp

45.

Solve the following for tan²θ:
1 + tan²θ = sec²θ

a)

tan²θ = sec²θ + 1

b)

tan²θ = sec²θ - 1

c)

tanθ = secθ - 1

d)

tan²θ = opp/adj

46.

What is csc(x) equivalent to?

a)

1/sin(x)

b)

1/tan(x)

c)

sin(x)

d)

1/cos(x)

47.

Please select the correct solution

a)

csc x

b)

sec x

c)

cot x

d)

tan x

48.

$\sin^2\ x+\cos^{2\ }\ x$

a)

$\cos\ x$

b)

$\frac{\sin\ x}{\cos\ x}$

c)

$1$

d)

$-\csc\ x$

49.

Simplify:
sinθcotθ

a)

sinθ

b)

tanθ

c)

cosθ

d)

secθ

50.

Simplify this to a basic trigonometry function:
tan(x)csc(x)

a)

tanx

b)

secx

c)

cotx

d)

cscx

Review and Trig Identities

Total questions: 50

Worksheet time: 30mins

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