SOLUTION: What are the solutions of sin (x - π) + 2 = 1 in [0, 2π)?

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Question 1141917: What are the solutions of sin (x - π) + 2 = 1 in [0, 2π)?
Answer by ikleyn(52915) About Me  (Show Source):
You can put this solution on YOUR website!
.

sin%28x-pi%29+%2B+2%7D%7C%7D%7D+=+1+++====%3E%0D%0A%0D%0A%0D%0A%7B%7B%7Bsin%28x-pi%29 = 1 - 2 = -1  ====>


x+-+pi = %283%2F2%29%2Api+%2B+k%2Api,  where k is any integer . . . ====>


x = %283%2F2%29%2Api+%2B+%28k%2B1%29%2Api,  where k is any integer . . . 


    And now my task is to choose "k" in a way to provide  x = %283%2F2%29%2Api+%2B+%28k%2B1%29%2Api  in the interval  [0,2pi).


For it, take k = -2;  you will get  x = %283%2F2%29%2Api+-+pi = pi%2F2.


ANSWER.  The solution is  x = pi%2F2.

         This solution is unique.

Solved.