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Use the circle unit to evaluate csc(-/2)

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The definition of the cosecant function is


\csc \theta=(1)/(\sin \theta)

Therefore,


\Rightarrow\csc (-(\pi)/(2))=(1)/(\sin (-(\pi)/(2)))

To find sin(-pi/2), use the diagram below.

Consider that the circumference has a radius equal to 1. Then, the coordinates of the orange point are (0,-1). Furthermore, the points on the circumference are given as (cos(theta), sin(theta)); therefore,


\begin{gathered} \Rightarrow(0,-1)=(\cos (-(\pi)/(2)),\sin (-(\pi)/(2))) \\ \Rightarrow\sin (-(\pi)/(2))=-1 \\ \Rightarrow\csc (-(\pi)/(2))=(1)/(-1)=-1 \\ \Rightarrow\csc (-(\pi)/(2))=-1 \end{gathered}

Thus, the answer is csc(-pi/2)=-1

Use the circle unit to evaluate csc(-/2)-example-1
User Sanderfish
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