math progress test 3

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Question description

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How many cycles does the sine function, y = 3 sin θ, have in the interval from 0 to 2

a. 1 b. 2 c. 3 d. 4

Find the measure of the angle in standard position.

1. 115°
2. −155°
3. 245°
4. −245°

Identify the amplitude and period of this function: y = 5 sin 2θ.

?

____ 3.

a.
b.
c.
d. 5,

Describe the phase shift and determine the value of “h” in the translation; y = cos (x

2, 2, 5,

____ 4.

d.

).

a.

b. c.

units to the left; h = − 1unittotheleft;h=−1

units to the right; h = units to the right; h =

____ 5.

Write this measure in degrees: 5 radians.

____ 6.

____ 7.

____ 8.

1. 36°
2. 900°
3. 1800°
4. 180°

Write this measure in degrees:

1. 157.5°
2. 315°
3. 205.7°
4. 70°

UseeithertheLawofSinesortheLawofCosines. In ,d=15in.,e=18in.,andf=10in.Findm .

a. b. c. d.

111.7° 56.3° 89.8° 24.5°

Find the exact sine value of −30° a.

b. c. d.

− −

____ 9.

Find the period of this function:

a. 2 b. 4 c. 6 d. 8

The period of a periodic function is 2.5 s. How many cycles does it go through in 20 s?

____ 10.

a.

1. 2 cycles
2. 50 cycles
3. 8 cycles

cycle

____ 11.

Verify this identity: sin θ csc θ = 1.

____ 12.

____ 13.

Describe the translation in y = cos (x – 3) + 2.

1. left 3 units; up 2 units
2. right 3 units; down 2 units
3. left 3 units; down 2 units
4. right 3 units; up 2 units

Identify the graph of this function from 0 to 2 a.

b.

c.

d.

: y = 2 cos x.

a.
b.
c.
d. 0=0

cos θ • = 1 •=1

sin θ • = 1

____ 14.

____ 15.

____ 16.

____ 17.

Two buildings on level ground are 150 feet apart. From the top edge of the shorter building, the angle of elevation to the top of the taller building is 32°, and the angle of depression to the bottom of the taller building is 40°. How tall is each building?

1. 96 ft, 176 ft
2. 260 ft, 419 ft
3. 126 ft, 220 ft
4. 223 ft, 317 ft

Simplify this expression: sin θ sec θ cot θ. a.

b.

sin2 θ c. 0

d. 1

Write this measure in degrees: −4

1. −720°
2. −1440°
3. −45°

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