Ok here's the problem: F: R^2 -> R^2 (t is theta) F(r,t) = (r*cos(t), r*sin(t)) What is F^-1(0,0)? I know the answer is {(0,0) | -inf < t < inf } but I'm not exactly sure how to get to that point.
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Originally Posted by merzbow Ok here's the problem: F: R^2 -> R^2 (t is theta) F(r,t) = (r*cos(t), r*sin(t)) What is F^-1(0,0)? I know the answer is {(0,0) | -inf < t < inf } but I'm not exactly sure how to get to that point. lets start with this consider so we would need to know when since cosine and sine are never zero at the same value of theta r must be zero. If that is the case then the equation is true for all values of theta so the inverse immage of (0,0) is
Ah, thanks man. I knew it was something easy, I just couldn't figure it out.
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