Modeling with Periodic Functions — Unit test Answers

Which values for have the same reference angles?

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

Which statement accurately describes how adding a number, n, to the function affects its graph?

What is the approximate length of arc s on the circle below? Use 3.14 for . Round your answer to the nearest tenth.

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

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

On a unit circle, the vertical distance from the x-axis to a point on the perimeter of the circle is twice the horizontal distance from the y-axis to the same point. What is sin?

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

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 , 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?

An angle that shares the same sine value of an angle that measures radians is located where?

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.

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

Henry is asked to find the exact value of . His steps are shown below.1. Subtract from as many times as possible: – = 2. Find the reference angle for : – = .3. The cosine value for is .4. The cosine value is positive because is in the first quadrant.Which of the following describes Henry’s errors?

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 ?

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 , what are the values of a and k?