SOLUTION: How do I algebraically solve for the general solution of {{{y=sin((pi/4)(x-6))=0.5}}}?

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Question 1104614: How do I algebraically solve for the general solution of y=sin%28%28pi%2F4%29%28x-6%29%29=0.5?
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The general solution for sin%28t%29+=+0.5 is %28pi%2F6%29%2B2k%28pi%29 or %285pi%2F6%29%2B2k%28pi%29.

So you want to solve
(1) %28pi%2F4%29%28x-6%29+=+%28pi%2F6%29%2B2k%28pi%29
and
(2) %28pi%2F4%29%28x-6%29+=+%285pi%2F6%29%2B2k%28pi%29

Solving either one for x is basic algebra. I'll do (1) and let you do (2)....

%28pi%2F4%29%28x-6%29+=+%28pi%2F6%29%2B2k%28pi%29
%28pi%2F4%29x-3pi%2F2+=+pi%2F6%2B2k%28pi%29 [distribute...]
%28pi%2F4%29x+=+3pi%2F2%2Bpi%2F6%2B2k%28pi%29+=+5pi%2F3%2B2k%28pi%29 [combine like terms...]
%281%2F4%29x+=+5%2F3%2B2k [divide out the common factor "pi"]
x+=+20%2F3%2B8k

Any value of x of the form (20/3)+8k, where k is an integer, is a solution to the given equation.