UNIT TEST REVIEW

Which of the following is the graph of y=sin(4(x-pi))? (starts at 0 touches 1 and -1 pi 2pi)

A

A student uses the equation mc013-1.jpg to represent the speed, s, in feet per second, of a toy car driving around a circular track having an angle of incline mc013-2.jpg, where mc013-3.jpg. To solve the problem, the student used the given value of mc013-4.jpg to find the value of mc013-5.jpg and then substituted the value of mc013-6.jpg in the equation above to solve for s. What is the approximate value of s, the speed of the car in feet per second?

A (5.3)

Henry is asked to find the exact value of cos10pi/3 . His steps are shown below.

A (The reference angle should be pi/3, and the sign of the value should be negative.)

Which statement accurately describes how adding a number, n, to the function f(x)=sin(x) affects its graph?

A (There is a vertical shift of n units.)

Which of the following is cot(0) sec(0) in simplified form?

A (csc 0)

The average daily temperature, t, in degrees Fahrenheit for a city as a function of the month of the year, m, can be modeled by the equation t=35cos(pi/6(m+3))+55, where m = 0 represents January 1, m = 1 represents February 1, m = 2 represents March 1, and so on. Which equation also models this situation?

A (t=-35sin(pi/6m)+55)

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

A (vertical compression of mc022-2.jpg, horizontal stretch to a period of mc022-3.jpg, vertical shift of 1 unit up, phase shift of mc022-4.jpg units left)

For which value of 0 is cot (0) undefined?

B (180)

Which function is the same as y=3cos(2(x+pi/2))-2?

B (y=-3sin(2(x+pi/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.

C (d=-2.75cos(4pi/31t))+6

What is the general equation of a sine function with an amplitude of 6, a period of pi/4, and a horizontal shift of pi/2?

C (y=6sin(8(x-pi/2)))

In a right triangle, cosA=0.352 and sinA=0.936. What is the approximate value of tanA

D (2.659)

The average daily temperature, t, in degrees Fahrenheit for a city as a function of the month of the year, m, can be modeled by the equation graphed below, where m = 0 represents January 1, m = 1 represents February 1, m = 2 represents March 1, and so on. If the equation is t=acos(pi/6(m+1))+k, what are the values of a and k?

D (a = -20; k = 60)

The graph of which function passes through (0,3) and has an amplitude of 3?

D (f(x)=3cos(x))

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 mc015-1.jpg. What is the height of the ball at its equilibrium?

D (k feet)