Exam 4: Graphing and Inverse Functions

The graph below is one complete cycle of the graph of an equation containing a trigonometric function. Find an equation to match the graph. If you are using a graphing calculator, graph your equation to verify that it is correct.

For the given equation, first identify the phase shift and then sketch one complete cycle of the graph. Graph y = cos x on the same coordinate system. ​

Use your graphing calculator to graph the pair of functions for . (Make sure your calculator is set to radian mode.) y = cos  Bx for B = 1, 3 ​

The graph below is one complete cycle of the graph of an equation containing a trigonometric function. Find an equation to match the graph. If you are using a graphing calculator, graph your equation to verify that it is correct.

The graph below is one complete cycle of the graph of an equation containing a trigonometric function. Find an equation to match the graph. If you are using a graphing calculator, graph your equation to verify that it is correct. ​

Evaluate the expression without using a calculator, and write your answer in radians. ​

The diameter of a Ferris wheel is 161 feet, it rotates at 0.05 revolutions per minute, and the bottom of the wheel is 7 feet above the ground. Find an expression that gives a passenger's height above the ground at any time t (in minutes)during the ride. Assume the passenger starts the ride at the bottom of the wheel. ​

Find the equation of the line. Write your answer in slope-intercept form, . ​

Identify the graph of the function y = 4sin 2 x ​

Graph one complete cycle for the function. Label the axes so that the amplitude (if defined)and period are easy to read. ​

Evaluate the expression without using a calculator, and write your answer in radians.

Use your graphing calculator to graph in degree mode. Use the graph with the appropriate command to evaluate the expression. ​

The graph below is one complete cycle of the graph of an equation containing a trigonometric function. Find an equation to match the graph. If you are using a graphing calculator, graph your equation to verify that it is correct.

The diameter of a Ferris wheel is 161 feet, it rotates at 0.05 revolutions per minute, and the bottom of the wheel is 8 feet above the ground. Find an expression that gives a passenger's height above the ground at any time t (in minutes)during the ride. Assume the passenger starts the ride at the bottom of the wheel.

Use your graphing calculator to graph in degree mode. Use the graph with the appropriate command to evaluate the expression. __________ °

The graph below is one complete cycle of the graph of an equation containing a trigonometric function. Find an equation to match the graph. If you are using a graphing calculator, graph your equation to verify that it is correct.

The graph below is one complete cycle of the graph of an equation containing a trigonometric function. Find an equation to match the graph. If you are using a graphing calculator, graph your equation to verify that it is correct. ​

Sketch one complete cycle of the following function by first graphing the appropriate sine or cosine curve and then using the reciprocal relationships. ​

The graph below is one complete cycle of the graph of an equation containing a trigonometric function. Find an equation to match the graph. If you are using a graphing calculator, graph your equation to verify that it is correct. ​ ​

Use your graphing calculator to graph the family of functions for  together on a single coordinate system. (Make sure your calculator is set to radian mode.) y = A sin  x for A = 1, 4, 6 ​