SOLUTION: How do you calculate the roots of the function f(x)=-2csc(x-pi/2)+4 in the interval [0,pi]?
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Question 597341: How do you calculate the roots of the function f(x)=-2csc(x-pi/2)+4 in the interval [0,pi]?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
\ =\ -2\csc\left(x\ -\ \frac{\pi}{2}\right)\ +\ 4\ \ )
in 
I presume you mean the zeros of the function since "roots" is really a term that is used with polynomial functions.
\ +\ 4\ =\ 0)
\ =\ -4)
\ =\ 2)
Cosecant is the reciprocal of sine
}\ =\ 2)
\ =\ \frac{1}{2})
\ =\ \frac{\pi}{6}\ \pm\ 2k\pi\ \ )
or 
So
which is in the given interval if and only if 
Hence,
Or
which is not in the given interval for any values of 
Therefore the solution set contains the single element 
John
My calculator said it, I believe it, that settles it
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