There are at least 3 different ways to solve the equation (csc^2(2theta)-1)^2 = 9. Use at least 2 different methods to solve for theta € [0,2pi) in both. Let v = 2theta in both methods. What interval is v in to get theta € [0,2pi)? One method should include a Phythagorean identity without factoring and the other should involve factoring, but not a Pythagorean identity and show all steps in each process, then illustrate on a unit circle. For each of the methods used, graph the trigonometric function with variable theta for [0,2pi) and with v for the interval found above on the same axes to demonstrate the difference in the period and then explain how they are related. While illustrating the solutions for both theta and v, you'll notice there should be the same number of solutions for both. Explain the relationship between them on each graph.
There are at least 3 different ways to solve the equation (csc^2(2theta)-1)^2 = 9. Use at least 2 different methods to solve for theta € [0,2pi) in both. Let v = 2theta in both methods. What interval is v in to get theta € [0,2pi)? One method should include a Phythagorean identity without factoring and the other should involve factoring, but not a Pythagorean identity and show all steps in each process, then illustrate on a unit circle. For each of the methods used, graph the trigonometric function with variable theta for [0,2pi) and with v for the interval found above on the same axes to demonstrate the difference in the period and then explain how they are related. While illustrating the solutions for both theta and v, you'll notice there should be the same number of solutions for both. Explain the relationship between them on each graph.
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