There are at least 3 ways to solve the equation (sec^2(2theta)-1)^2 = 9. Use at least two of the ways and solve for theta within the interval of [0,2pi) and let v = 2theta in both solutions while making sure to use one method that includes the Pythagorean identity with no factoring and the other method that uses factoring, but not a Pythagorean identity. Show each step in the process and then illustrate on a unit circle. Then graph both trigonometric functions with variable theta for [0,2pi) and with v for the interval found earlier on the same set of axes to illustrate the difference in the period and then explain how the graphs are related. Then illustrate the solutions for both theta and v on the graphs of both trig functions and explain the relationships between the 2 solutions on each graph.
There are at least 3 ways to solve the equation (sec^2(2theta)-1)^2 = 9. Use at least two of the ways and solve for theta within the interval of [0,2pi) and let v = 2theta in both solutions while making sure to use one method that includes the Pythagorean identity with no factoring and the other method that uses factoring, but not a Pythagorean identity. Show each step in the process and then illustrate on a unit circle. Then graph both trigonometric functions with variable theta for [0,2pi) and with v for the interval found earlier on the same set of axes to illustrate the difference in the period and then explain how the graphs are related. Then illustrate the solutions for both theta and v on the graphs of both trig functions and explain the relationships between the 2 solutions on each graph.
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