Quiz about 10054 Unit 3 Review (Topics 18-23): Trigonometry

Question 1

$$ an\left( heta ight)$$ represents...

Accepted Answer

the ratio of coordinates: $$\frac{y}{x}$$

Answer

the $$x$$ coordinate on the unit circle

Answer

the $$y$$ coordinate on the unit circle

Question 2

$$\sin\left(120\degree\right)=$$

Accepted Answer

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

Answer

$$\frac{\sqrt[]{2}}{2}$$

Answer

$$-\frac{1}{2}$$

Answer

$$\frac{1}{2}$$

Question 3

$$\sin\left(\frac{\pi}{4}\right)=$$

Accepted Answer

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

Answer

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

Answer

$$\frac{1}{2}$$

Answer

$$1$$

Answer

$$0$$

Question 4

Evaluate $$\sin\left(\frac{\pi}{2}\right)$$

Accepted Answer

$$1$$

Answer

$$-\frac{1}{2}$$

Answer

$$\frac{1}{2}$$

Answer

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

Answer

$$-1$$

Question 5

$$\sin\left(-135\degree\right)=$$

Accepted Answer

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

Answer

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

Answer

$$-\frac{1}{2}$$

Answer

$$\frac{1}{2}$$

Question 6

$$\cos\left(\frac{7\pi}{6}\right)=$$

Accepted Answer

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

Answer

$$\frac{\sqrt[]{2}}{2}$$

Answer

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

Answer

$$-\frac{1}{2}$$

Question 7

$$\cos\left(0\right)=$$

Accepted Answer

$$1$$

Answer

$$0$$

Answer

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

Answer

$$\frac{1}{2}$$

Answer

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

Question 8

Exact value of $$\sin\left(-\frac{5\pi}{3}\right)$$

Accepted Answer

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

Answer

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

Answer

$$\frac{1}{2}$$

Answer

$$-\frac{1}{2}$$

Question 9

Evaluate $$\sin\left(\frac{23\pi}{6}\right)$$

Accepted Answer

$$-\frac{1}{2}$$

Answer

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

Answer

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

Answer

$$\sqrt{3}$$

Question 10

Exact value of $$ an\ \left(\frac{5\pi}{6} ight)$$

Accepted Answer

$$\frac{-\ \sqrt[]{3}}{3}$$

Answer

$$-\ \sqrt[]{3}$$

Answer

$$\frac{1}{2}$$

Answer

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

Answer

$$\frac{\sqrt[]{3}}{3}$$

Question 11

$$ an\left(210\degree ight)=$$

Accepted Answer

$$\frac{\sqrt[]{3}}{3}$$

Answer

$$\frac{\sqrt[]{2}}{2}$$

Answer

$$-\sqrt[]{3}$$

Answer

$$-\frac{1}{2}$$

Question 12

$$ an(-\pi)=$$

Accepted Answer

0

Answer

undefined

Answer

1

Answer

-1

Question 13

Evaluate the given expression using only your unit circle. Give answers in degrees!

$$\cos^{-1}\left(\frac{-1}{2}\right)$$ =___ $$\degree$$

Accepted Answer

120

Answer

30

Answer

60

Answer

150

Question 14

Evaluate the given expression using only your unit circle. Give answers in degrees!

$$ an^{-1}\left(-1 ight)$$ =___ $$\degree$$

Accepted Answer

-45

Answer

45

Answer

315

Answer

90

Question 15

Use the unit circle to match the angle measure: $$\cos\left(\frac{10\pi}{3}\right)$$

Accepted Answer

$$-\frac{1}{2}$$

Answer

$$\frac{\sqrt[]{2}}{2}$$

Answer

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

Answer

$$\frac{1}{2}$$

Question 16

Evaluate the given expression using only your unit circle. Give answers in degrees!

$$\sin^{-1}\left(-1\right)$$ =___ $$\degree$$

Accepted Answer

-90

Answer

45

Answer

90

Answer

0

Question 17

If the angle $$ heta$$ is in quadrant II and the $$\sin heta=\frac{5}{7}$$ which of the following represents the $$\cos heta$$ ?

Accepted Answer

$$\frac{-2\ \ \sqrt[]{6}}{7}$$

Answer

$$\frac{-7}{5}$$

Answer

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

Answer

$$\frac{2\ \sqrt[]{6}}{7}$$

Question 18

What quadrant is $$ heta=-\frac{2\pi}{3}$$ in?

Accepted Answer

III

Answer

I

Answer

II

Answer

IV

Question 19

What is the period of the function $$y=3\sin\left(2x-\frac{2\pi}{3}\right)$$ ?

Period $$=\frac{2\pi}{b}$$

Accepted Answer

$$\pi$$

Answer

$$2\pi$$

Answer

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

Answer

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

Question 20

Use the unit circle to match the angle measure: $$\sin\pi$$

Accepted Answer

$$0$$

Answer

undefined

Answer

$$-1$$

Answer

$$1$$

Question 21

What is the phase shift (horizontal shift) of the function $$y=3\sin\left(2x-\frac{2\pi}{3}\right)$$ ?

Phase Shift $$=\frac{c}{b}$$

Accepted Answer

$$\frac{\pi}{3}$$ units to the right

Answer

$$\frac{\pi}{3}\ $$ units to the left

Question 22

Simplify the trig expression.

Accepted Answer

tanx

Answer

sinx

Answer

cosx

Answer

cotx

Question 23

Use the unit circle to match the angle measure: $$\cos\left(\frac{7\pi}{4}\right)$$

Accepted Answer

$$\frac{\sqrt[]{2}}{2}$$

Answer

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

Answer

$$-\frac{1}{2}$$

Answer

$$\frac{1}{2}$$

Question 24

What is the phase shift (horizontal shift) of the function $$y=\cos\left(2x-14\pi\right)$$ ?

Accepted Answer

$$7\pi$$ units to the right

Answer

$$\pi$$ units to the right

Answer

$$14\pi$$ units to the right

Answer

$$14\pi$$ units to the left

Question 25

Which graph represents the function $$f\left(x\right)=-2\cos x+1$$ ?

Accepted Answer

Option A is correct

Answer

B.

Answer

C.

Answer

D.

Question 26

What is csc(x) equivalent to?

Accepted Answer

$$\frac{1}{\sin x}$$

Answer

$$\frac{1}{ an x}$$

Answer

sin(x)

Answer

$$\frac{1}{\cos x}$$

Question 27

Simplify.

Accepted Answer

sec2 x

Answer

csc2 x

Answer

cot2 x

Answer

sin2 x

Question 28

Simplify.
cos²x + sin ²x=

Accepted Answer

1

Answer

csc²x + sec²x

Answer

sin 2 x

Answer

1 - sin 2 x

Question 29

Simplify the trig expression.

Accepted Answer

-1

Answer

1

Answer

-tanx

Answer

tanx

Question 30

Simplify

Accepted Answer

tan x

Answer

csc x

Answer

sec x

Answer

cot x

Question 31

Simplify.

Accepted Answer

cos x

Answer

sin x

Answer

tan x

Answer

1

Question 32

Simplify $$\left(\csc x+1\right)\left(\csc x-1\right)$$

Accepted Answer

$$\cot^2x$$

Answer

$$\csc^2x+1$$

Answer

$$	an^2x$$

Answer

$$2\csc x$$

Question 33

Question 33.

Accepted Answer

cot(u)

Answer

sec(u)

Answer

cos(u)

Answer

csc(u)

Answer

sin(u)

Question 34

Question 34.

Accepted Answer

csc(u)

Answer

cos(u)

Answer

tan(u)

Answer

sin(u)

Answer

cot(u)

Question 35

Question 35.

Accepted Answer

tan(u)

Answer

sec(u)

Answer

cos(u)

Answer

sin(u)

Answer

csc(u)

Question 36

Simplify: $$\left(\cos\ θ\right)\left(\sec\ θ-\cosθ\right)$$

Accepted Answer

$$\sin^2θ$$

Answer

$$\cos^2θ$$

Answer

$$\csc^2 heta$$

Answer

$$\sec^2 heta$$

Question 37

Simplify: $$\sec x- an x\sin x$$

Accepted Answer

$$\cos x$$

Answer

$$\sin x$$

Answer

$$\csc x$$

Answer

$$\sec x$$

Question 38

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

Accepted Answer

$$\cos^3x$$

Answer

$$\sin^2x$$

Answer

$$\cos^2x$$

Answer

$$\sin^3x$$

Question 39

Simplify: $$\frac{\cos^2\left(-x\right)\csc x}{\cot x}$$

Accepted Answer

$$\cos x$$

Answer

$$-\sin x$$

Answer

$$-\cos x$$

Answer

$$\sin x$$

Question 40

$$\cos\left(- heta ight)=$$

Accepted Answer

$$\cos\left( heta ight)$$

Answer

$$-\cos\left( heta ight)$$

Answer

$$-\cos\left(- heta ight)$$

Question 41

$$\sin\left(- heta ight)=$$

Accepted Answer

$$-\sin\left( heta ight)$$

Answer

$$\sin\left( heta ight)$$

Answer

$$-\sin\left(- heta ight)$$

Question 42

$$ an\left(- heta ight)=$$

Accepted Answer

$$- an\left( heta ight)$$

Answer

$$ an\left( heta ight)$$

Answer

$$- an\left(- heta ight)$$

Question 43

Solve equation for $$0\le heta<2\pi$$ .
$$3\sin^2 heta=7\sin^2 heta+4\sin heta+1$$

Accepted Answer

$$ heta=\frac{7\pi}{6},\frac{11\pi}{6}$$

Answer

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

Answer

$$ heta=0,\frac{\pi}{3},\frac{5\pi}{3}$$

Answer

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

Question 44

Solve over the interval $$\left[0,2\pi ight)$$

$$3\sin heta=\sqrt[]{3}\cos heta$$

Accepted Answer

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

Answer

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

Answer

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

Answer

$$\frac{\pi}{6},\frac{5\pi}{6},\frac{7\pi}{6},\frac{11\pi}{6}$$

Question 45

Solve:

$$2\cos2x+3=2$$

Accepted Answer

$$x=\frac{\pi}{3}+n\pi;\ x=\frac{2\pi}{3}+n\pi$$

Answer

$$x=\frac{2\pi}{3}+2n\pi;\ x=\frac{4\pi}{3}+2n\pi$$

Answer

$$x=\frac{\pi}{3};\ x=\frac{2\pi}{3}$$

Answer

$$x=-\frac{1}{4}$$

Question 46

Choose the correct ratio.

Accepted Answer

cos(37)=x/14

Answer

sin(37)=x/14

Answer

tan(37)=x/14

Answer

sin(37)=14/x

Question 47

Which trigonometric ratio should you use?

Accepted Answer

Tangent Ratio

Answer

Sine Ratio

Answer

Cosine Ratio

Answer

Any ratio

Question 48

Which trigonometric ratio should you use?

Accepted Answer

Any ratio

Answer

Tangent Ratio

Answer

Sine Ratio

Answer

Cosine Ratio

Question 49

Sine or Cosine?

Accepted Answer

y=sinx

Answer

y=cosx

Question 50

What is the equation of the graph?

Accepted Answer

y = 2 sin x

Answer

y = 2 cos x

Answer

y = sin x

Answer

y = sin 2x

Question 51

Find the measure of the missing angle.

Accepted Answer

26o

Answer

64o

Answer

61o

Answer

.008o

Question 52

Solve for x. Round to the nearest tenth.

Accepted Answer

7.5

Answer

34.1

Answer

14.1

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