Trigonometric Function Homework: Solving sin^2 (x - pi/4) = 1

AI Thread Summary
To solve the equation sin^2(x - pi/4) = 1, recognize that the expression being squared can equal either 1 or -1. This leads to two separate equations: sin(x - pi/4) = 1 and sin(x - pi/4) = -1. For each case, determine the values of x by applying the inverse sine function and considering the periodic nature of the sine function. After solving both equations, combine all solutions to find the complete set of answers. The key is to account for the periodicity of the sine function when determining the final solutions.
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Homework Statement


Pardon me first of all for any mistakes, I study in a French school so I might use incorrect terms

I have to find the solutions for the following formula:

sin^2 ( x - pi/4 ) = 1


Homework Equations


None?


The Attempt at a Solution


I've mostly only worked with regular sins, not those that are to the power of n..

most of the time i'd isolate everything then do arcsin(...) and so on but I am not sure what to do exactly here.
 
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You have something being squared to produce 1. That means the thing being squared is either 1 or -1. This gives you two equations involving sin(x - pi/4). Find solutions for each one.
 
if you take the square root of both sides, on the left side you will get sin(x- pi/4)

and +/- 1 on the right side. Take each case and find x, then combine all of the answers.
 
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