SOLUTION: How can you prove that there does not exist an angle theta such that costheta(sintheta)= 2/3

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Question 680889: How can you prove that there does not exist an angle theta such that costheta(sintheta)= 2/3
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'm using x instead of theta

cos(x)*sin(x) = 2/3

(1/2)*sin(2x) = 2/3

sin(2x) = 2*2/3

sin(2x) = 4/3

2x = arcsin(4/3)

Since the domain of the arcsine function is -1 <= x <= 1 and since 4/3 is greater than 1, this means that there are no solutions.