Free Printable Unit 1: Intro to Trig Study Guide

1.

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

2.

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

3.

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

4.

sin π =

a)

0

b)

1

c)

-1

d)

undefined

5.

cos π =

a)

0

b)

1

c)

-1

d)

undefined

6.

Based on the unit circle, what is the value of sin?

a)

y

b)

x

c)

x/y

d)

y/x

7.

Based on the unit circle, what is the value of cos?

a)

y

b)

x

c)

x/y

d)

y/x

8.

Based on the unit circle, what is the value of tan?

a)

y/r

b)

x/r

c)

r/y

d)

y/x

9.

Using the Unit Circle, find the exact value of this trig function.

a)

b)

c)

d)

e)

The correct answer is not listed

10.

Using the Unit Circle, find the exact value of this trig function.

a)

1

b)

0

c)

-1

d)

undefined

e)

The correct answer is not listed

11.

tan 2π =

a)

0

b)

1

c)

-1

d)

undefined

12.

Using (-3, 1) as the terminal side, what is $\cos\left(\theta\right)$ ?

a)

$-3$

b)

$-\frac{3\sqrt{10}}{10}$

c)

$1$

d)

$\frac{\sqrt{10}}{10}$

13.

If $\sin\ \left(\theta\right)=-\frac{1}{3}$ , what is $\tan\left(\theta\right)$ in quadrant 4?

a)

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

b)

$2\sqrt{2}$

c)

$-2\sqrt{2}$

d)

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

14.

Using your unit circle, what is $\cot\left(-5\pi\right)$ ?

a)

$0$

b)

$1$

c)

$-1$

d)

undefined

15.

$If\ \sec\left(\theta\right)=-4,\ what\ is\ \sin\left(\theta\right)\ in\ quadrant\ 2?$

a)

$-\frac{\sqrt{15}}{4}$

b)

$\frac{\sqrt{15}}{4}$

c)

$\frac{1}{4}$

d)

$-\frac{1}{4}$

16.

Choose all the trigonometric ratios below that have a solutions of $-\frac{1}{2}$ .

a)

$\sin\left(330^o\right)$

b)

$\cos\left(120^o\right)$

c)

$\sin\left(-30^o\right)$

d)

$\cos\left(240^o\right)$

e)

$\sin\left(-240^o\right)$

17.

sin π/4

a)

√2∕2

b)

1/2

c)

√3/2

d)

0

18.

What is the exact coordinates of 3π/4 on the unit circle?

a)

(−√2∕2, √2∕2)

b)

(−√2∕2, −√2∕2)

c)

(−√3∕2, −√2∕2)

d)

(√2∕2, −√2∕2)

19.

Find the exact value.

\sec\left(\frac{3\pi}{2}\right)

a)

$0$

b)

undefined

c)

1

d)

-1

20.

Find the exact value.

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

a)

$-\frac{1}{2}$

b)

$\frac{1}{2}$

c)

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

d)

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

21.

What radian measure corresponds to the given point?

a)

$\frac{\pi}{4}$

b)

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

c)

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

d)

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

22.

Determine which quadrant or axes the angle would terminate in if:

tan>0 and sin<0

a)

Q1

b)

Q2

c)

Q3

d)

Q4

e)

+y-axis

23.

Determine which quadrant or axes the angle would terminate in if:

sec>0 and cot>0

a)

Q1

b)

Q2

c)

Q3

d)

Q4

e)

- x-axis

24.

Which angle(s) satisfies tan=-1

a)

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

b)

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

c)

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

d)

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

25.

Find tanΘ if cosΘ= -^√3/₂ and π < Θ < ^3π/₂

a)

tan Θ = ^√3/₃

b)

tan Θ = 1

c)

tan Θ = -^√3/₃

d)

tan Θ = -1

26.

Find the ratio for sinA. (Reduce the fraction)

a)

36/27

b)

4/5

c)

36/45

d)

3/5

27.

What is the cosine of angle P?

a)

p/q

b)

q/r

c)

p/r

d)

r/q

28.

Find a coterminal angle to -27°.

a)

-387°

b)

27°

c)

323°

d)

-393°

29.

In which quadrant would you find an angle measuring -740°

a)

1

b)

2

c)

3

d)

4

30.

What is the reference angle for 125°?

a)

235°

b)

125°

c)

75°

d)

55°

31.

What is the reference angle?

a)

43

b)

-43

c)

47

d)

-47

32.

Simplify by rationalizing the denominator

a)

b)

c)

d)

33.

Simplify.

a)

A

b)

B

c)

C

d)

D

34.

Simplify:

4√75

a)

4√5

b)

12√5

c)

20√3

d)

7√3

35.

Which of the following is closest to the measure of the angle shown?

a)

7/10 π

b)

3/8 π

c)

7/20 π

d)

3/2 π

36.

Convert 100⁰ to radians

a)

5π/9

b)

π/2

c)

5π/8

d)

5π/6

37.

Convert the following to degrees:
-8π/5 radians

a)

-288⁰

b)

-260⁰

c)

-275⁰

d)

$-112.5\degree$

38.

a)

π/2

b)

π/8

c)

π/6

d)

π/4

39.

a)

2π/4

b)

3π/4

c)

5π/6

d)

7π/6

40.

a)

5π/6

b)

7π/4

c)

10π/6

d)

11π/6

41.

What is the exact coordinates of 3π/4 on the unit circle?

a)

(−√2∕2, √2∕2)

b)

(−√2∕2, −√2∕2)

c)

(−√3∕2, −√2∕2)

d)

(√2∕2, −√2∕2)

42.

For what angles are sine and cosine the same?

a)

0^o

b)

45^oand 135⁰

c)

45^oand 225⁰

d)

45^oand 315⁰

43.

What are the coordinates of 210° on the unit circle?

a)

(−√3/2, −1/2)

b)

(√3/2, −1/2)

c)

(−√3/2, 1/2)

d)

(−1/2,−√3/2 )

44.

If θ is an angle in Quadrant IV, which trig ratio(s) will be positive

a)

sin θ

b)

cos θ

c)

tan θ

d)

cos θ and tan θ

45.

Let (-4, 3) be a point on the terminal side of θ. Which of the following is FALSE?

a)

cot θ = -4/3

b)

tan θ = -3/4

c)

sin θ = 3/5

d)

cos θ = 4/5

46.

sin(11π/3) =

a)

sqrt(3)/2

b)

- sqrt(3)/2

c)

1/2

d)

-1/2

47.

What radian measure corresponds to the given point?

a)

π/4

b)

3π/2

c)

5π/4

d)

7π/3

48.

Using your unit circle, what is $\csc\left(-\frac{7\pi}{3}\right)$ ?

a)

$2$

b)

$-2$

c)

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

d)

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

49.

Given an angle whose terminal side lies at

\left(-2,5\right)

, what is the value of

\cos\theta

?

a)

$-\frac{\sqrt{29}}{2}$

b)

$-\frac{2\sqrt{29}}{29}$

c)

$-\frac{\sqrt{21}}{2}$

d)

$\frac{2\sqrt{29}}{29}$

50.

which two angles

$0\le\theta\le2\pi$ does $\cot\theta=-\frac{\sqrt{3}}{3}$

a)

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

b)

$\frac{2\pi}{3}and\ \frac{5\pi}{3}$

c)

$\frac{5\pi}{6}and\ \frac{7\pi}{6}$

d)

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

e)

none of these choices

Unit 1: Intro to Trig Study Guide

Total questions: 50

Worksheet time: 1hrs 20mins

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