Evaluate the $csc(heta)$ of an angle $heta$ in the unit circle when its $sin(heta)$ is equal to a rational value

To evaluate $\csc (\theta )$ when $\sin (\theta )$ is a rational value, let

To evaluate $csc(heta)$ given $sin(heta)=frac35$:

Since $csc(heta)=frac1sin(heta)$:

$csc(heta)=frac53$

Given $sin(heta)=frac35$, calculate $csc(heta)=frac1sin(heta)$:

$csc(heta)=frac53$

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