SOLUTION: If sin3y = cos2y and 0°≤y≤90°, find the values of y.

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Question 1207451: If sin3y = cos2y and 0°≤y≤90°, find the values of y.
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
sin(3y)=cos(2y),   0%5Eo%3C=y%3C=90%5Eo




For the case 

cos%282y%29=cos%2890%5Eo-3y%2B360%5Eo%2An%29
2y+=+90%5Eo-3y%2B360%5Eo%2An
which simplifies to

5y=90%5Eo%2B360%5Eo%2An
y=18%5Eo%2B72%5Eo%2An

This gives us the solutions 18o, 90o, for n=0 and n=1

However, this may not be all possible solutions 0%5Eo%3C=y%3C=90%5Eo

We must also consider the case

cos%282y%29=cos%283y-90%5Eo%2B360%5Eo%2An%29
2y+=+3y-90%5Eo%2B360%5Eo%2An
which simplifies to

-y=-90%5Eo%2B360%5Eo%2An
y=90%5Eo-360%5Eo%2An

We get only a repeat of the solution 90o for n=0 

18o, 90o are the only solutions 

Edwin