Solve E^x = k/c sin^2(x) Homework

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Homework Statement



e^x = \frac {k}{c}sin^2(y) solving for t

i thought it was t=arcsin(\sqrt{\frac{ce^x}{k}})

but my calc is saying like the answer above + ln4*pi + pi.
 
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er, where is there a "t" in your expression? do you mean t instead of y? or is y a function of t? if the y is supposed to be a t, you are most certainly right, otherwise, we are missing information
 
squaremeplease said:

Homework Statement



e^x = \frac {k}{c}sin^2(y) solving for t

i thought it was t=arcsin(\sqrt{\frac{ce^x}{k}})

but my calc is saying like the answer above + ln4*pi + pi.
y= arcsin(\sqrt{\frac{ce^x}{k}}))
is a solution buy sine is a periodic function so there are other values of y that will give the same value.
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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