Answers S1S-OC Pre-Calculus A E3700 - AGUnit Test

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Consider the function y = cos(x). Which change would increase the period by a factor of 3?

Multiply cos(x) by

Multiply cos(x) by 3.

Multiply x by

Multiply x by 3.

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In which quadrant(s) is csc(x) positive?

quadrant I only

quadrant II only

quadrants I and II

quadrants I and III

At a certain location, the number of hours of sunlight is modeled by y = where x represents the number of weeks after the summer solstice.Based on the model, what is the minimum number of hours of sunlight at this location?

3.2

5.6

6.4

13.0

How many degrees is radians?

84.375°

93.75°

168.75°

337.5°

During high tide around 11:00 p.m., the water level is 3 feet above a marker on a pier. The following day, during low tide around 5:12 a.m., the water level has dropped 3 feet below the marker. The height of the water is modeled by the function , where x is the time in hours since 11:00 p.m.What is the height of the water at 2:15 a.m.?

0.22 feet below the marker

0.07 feet below the marker

1.26 feet above the marker

1.39 feet above the marker

The table shows the temperatures in degrees Celsius, y, inside a shed at x hours past noon. The maximum and minimum temperatures are shown.

y = 3 cosine (StartFraction pi Over 12 EndFraction x minus StartFraction pi Over 3 EndFraction) + 17

y = 3 cosine (StartFraction pi Over 12 EndFraction x minus StartFraction pi Over 4 EndFraction) + 17

y = 6 cosine (StartFraction pi Over 12 EndFraction x minus StartFraction pi Over 3 EndFraction) + 17

y = 6 cosine (StartFraction pi Over 12 EndFraction x minus StartFraction pi Over 4 EndFraction) + 17

Which expression is equivalent to 30°?

Inverse of cosine (StartFraction StartRoot 3 EndRoot Over 2 EndFraction)

Inverse of sine (StartFraction StartRoot 3 EndRoot Over 2 EndFraction)

Sine (StartFraction StartRoot 3 EndRoot Over 2 EndFraction)

Cosine (StartFraction StartRoot 3 EndRoot Over 2 EndFraction)

Review the graph.

y = tanx

y = cosx

y = tan-1x

y = cos-1x

Suppose tan(b) = –2, and the terminal side of b is located in quadrant II. What is cot(b)?

–2

Negative one-half

One-half

Which functions are symmetric with respect to the origin?

y = arcsinx and y = arccosx

y = arccosx and y = arctanx

y = arctanx and y = arccotx

y = arcsinx and y = arctanx

The function g(x) represents f(x) = after translating units left and 4 units up.Which equation represents g(x)?

g (x) = 9 cosine (x minus StartFraction pi Over 3 EndFraction) minus 1

g (x) = 9 cosine (x minus StartFraction pi Over 3 EndFraction) + 7

g (x) = 9 cosine (x minus StartFraction 2 pi Over 3 EndFraction) minus 1

g (x) = 9 cosine (x minus StartFraction 2 pi Over 3 EndFraction) + 7

A seat on a Ferris wheel is level with the center of the wheel. The diameter of the wheel is 200 feet. Suppose the wheel rotates 60°, causing the height of the seat to decrease. How much closer to the ground is the seat after the rotation?

50 feet

feet

100 feet

feet

Over which interval is the graph of y = cos(x) strictly increasing?

0 less-than x less-than StartFraction pi Over 2 EndFraction

0 < x < π

StartFraction pi Over 2 EndFraction less-than x less-than StartFraction 3 pi Over 2 EndFraction

π < x < 2π

Let a function y represent the water level in a harbor measured in meters, and let x represent the number of hours since high tide. At time x = 0, the water level is 19.5 meters (a maximum). At time x = 6.26 hours, the water level is 10.5 meters (a minimum). The period of the function is 12.5 hours.After how many hours is the water expected to reach a depth of 17 meters for the first time? Round to the nearest tenth of an hour.

2.2 hours

6.3 hours

12.1 hours

12.5 hours

Suppose the function h(x) = sinx is translated units left and 11 units down. Which graph represents the result?

On a coordinate plane, a function has a maximum of negative 10 and minimum of negative 12. It completes one period at 2 pi. It decreases through the y-axis at (0, negative 11).

On a coordinate plane, a function has a maximum of negative 10 and minimum of negative 12. It completes one period at 2 pi. It crosses the y-axis at (0, negative 10).

On a coordinate plane, a function has a maximum of negative 10 and minimum of negative 12. It completes one period at 2 pi. It increases through the y-axis at (0, negative 11).

On a coordinate plane, a function has a maximum of negative 10 and minimum of negative 12. It completes one period at 2 pi. It crosses the y-axis at (0, negative 12).

Review the graph.

y = –3cos(x)

y = –3sin(x)

y = 3cos(x)

y = 3sin(x)

The position of a paddle on a waterwheel after t seconds is modeled by f(t) = . A positive function value indicates the paddle is above the waterline, while a negative value indicates the paddle is below the waterline.What is the initial position of the paddle?