Transformations of Functions — Unit test

Question 1

What are the exact values of the six trigonometric functions for radians?

Revolt · Accepted Answer

sine (Negative StartFraction 7 pi Over 6 EndFraction) = one-half; cosine (Negative StartFraction 7 pi Over 6 EndFraction) = Negative StartFraction StartRoot 3 EndRoot Over 2 EndFraction; tangent (Negative StartFraction 7 pi Over 6 EndFraction) = Negative StartFraction StartRoot 3 EndRoot Over 3 EndFraction. Cosecant (Negative StartFraction 7 pi Over 6 EndFraction) = 2; secant (Negative StartFraction 7 pi Over 6 EndFraction) = Negative StartFraction 2 StartRoot 3 EndRoot Over 3 EndFraction; Cotangent (Negative StartFraction 7 pi Over 6 EndFraction) = Negative StartRoot 3 EndRoot

Question 2

Which of the following are in correct order from greatest to least?

Revolt · Accepted Answer

330°, , , ,

Question 3

Which of the following is the graph of ?

Revolt · Accepted Answer

On a coordinate plane, a curve crosses the y-axis at (0, 0). It has a maximum of 1 and a minimum of negative 1. It goes through 2 cycles at pi.

Question 4

The depth of the water at the end of a pier changes periodically along with the movement of tides. On a particular day, low tides occur at 12:00 a.m. and 3:30 p.m., with a depth of 3.25 meters, while high tides occur at 7:45 a.m. and 11:15 p.m., with a depth of 8.75 meters. Which of the following equations models d, the depth of the water in meters, as a function of time, t, in hours? Let t = 0 be 12:00 a.m.

Revolt · Accepted Answer

d = negative 2.75 cosine (StartFraction 4 pi Over 31 EndFraction t) + 6

Question 5

How long is the arc intersected by a central angle of radians in a circle with a radius of 6 ft? Round your answer to the nearest tenth. Use 3.14 for .

Revolt · Accepted Answer

6.3 ft

Question 6

Which transformations are needed to change the parent sine function to the sine function below?

Revolt · Accepted Answer

vertical compression of , horizontal stretch to a period of , vertical shift of 1 unit up, phase shift of units left

Question 7

A function is graphed on a coordinate grid. As the domain values approach infinity, the range values approach infinity. As the domain values approach negative infinity, the range values approach negative infinity. To which family of functions might the described function belong?

Revolt · Accepted Answer

cube root

Question 8

Melanie simplified the expression as shown below.Step 1:Step 2:Step 3:Step 4:In which step did Melanie make the first error, and which expression should she have written in that step?

Revolt · Accepted Answer

step 4; csc(x)

Question 9

The height, h, in feet of a ball suspended from a spring as a function of time, t, in seconds can be modeled by the equation . What is the height of the ball at its equilibrium?

Revolt · Accepted Answer

k feet

Question 10

Which measure is of an angle that is coterminal with a 95° angle?

Revolt · Accepted Answer

95° – (1,080n)°, for any integer n

Transformations of Functions — Unit test Answers

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