SOLUTION: Hello, I need help solving this trigonometric equation.The question is: solve the following question for θ. Unless otherwise specified, give all solutions as exact radian meas

Algebra ->  Trigonometry-basics -> SOLUTION: Hello, I need help solving this trigonometric equation.The question is: solve the following question for θ. Unless otherwise specified, give all solutions as exact radian meas      Log On


   

Question 1092858: Hello, I need help solving this trigonometric equation.The question is: solve the following question for θ. Unless otherwise specified, give all solutions as exact radian measurements such that 0 ≤ θ < 2pi.
1. sin^4 2θ -2sin^2 2θ= -1
I hope this isn't too confusing. I appreciate any time and effort that you put into solving this. Thank you in advance for your help!
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
sin%5E4%282theta%29-2sin%5E2%282theta%29 = -1  ====>

sin%5E4%282theta%29-2sin%5E2%282theta%29+%2B+1 = 0  ====>

%28sin%5E2%282theta%29+-+1%29%5E2 = 0  ====>

sin%5E2%282theta%29+-+1 = 0  ====>

%28sin%282theta%29+-+1%29%2A%28sin%282theta%29%2B1%29 = 0  ====>


There are two ways to continue:


1)   sin%282theta%29 = 1  ====>  theta = pi%2F4  and/or  theta = 5pi%2F4.


2)   sin%282theta%29 = -1  ====>  theta = 3pi%2F4  and/or  theta = 7pi%2F4.


Answer.  The original equation has 4 roots in the interval [0,2pi):


         theta = pi%2F4,  3pi%2F4,  5pi%2F4  and  7pi%2F4.