An angle between 0 degrees and 360 degrees has a cosecant of -1.

a) is this enough info to determine a unique solution? if yes, explain why. if no, what other info is required?

b) determine the angle or angles

thank you!

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We are given an angle `0<=theta<=360^@` and `csctheta=-1` .

(a) Is there a unique solution? If `csctheta=-1` then `sintheta=-1` . On the interval `[0,360]` this occurs at `theta=270^@` .

This is the unique solution.

(b) The angle is `270^@`

First answer.

It is ot enough to determine unique solution It is periodic function.

`cosec(x)=1/sin(x)`

sin(x) has unique solution in interval `[-pi/2,pi/2]`

cosec(x) is not defined if x=0

cosec(x) has unique solution in `[-pi/2,0)U(0pi/2]`

other informatins are required characteristic of function

`cosec(x)=-1`

`1/sin(x)=-1`

`sin(x)=-1`

`x=npi+(-1)^n(3pi/2)`

`n=0`

`x=(3pi)/2`

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