Algebra 2 Test Review: Trigonometric Functions

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?

5.3

If a vertical line is dropped from the x-axis to the point (12, -9) in the diagram below, what is the value of sec(∅)?

5/4

Which of the following is true for f(x) = -2sin(x) - 3?

The amplitude of the function is 2.

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

There is a vertical shift of n units.

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 mc026-1.jpg, 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

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 mc014-1.jpg, what are the values of a and k?

a = -20; k = 60

A student is given that point P(a, b) lies on the terminal ray of angle mc026-1.jpg, which is between mc026-2.jpg radians and 2mc026-3.jpg radians. The student uses the steps below to find cos mc026-4.jpg. Which of the following explains whether the student is correct?

a. The student made an error in step 3 because a is positive in Quadrant IV; therefore, mc026-9.jpg.

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(π/31t)+6

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

csc(∅)

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

f(x)=3cosx

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 h=asin(b(t-h))+k. What is the height of the ball at its equilibrium?

k feet

Which formula gives the zeros of y = sin(x)?

kπ for any integer k

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

vertical compression of 1/2, horizontal stretch to a period of 4π, vertical shift of 1 unit up, phase shift of π units left

An angle in standard position measures pi/2 radians, and P(0, 1) is on the terminal side of the angle. What is the value of the cosine of this angle?

0

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

180 °