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Determine the values of the six trigonometric functions of (- pi / 2 )

with work shown please.

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Answer:


\circ \quad sin\left(-(\pi)/(2)\right) = -1\\\\


\circ \quad \cos \left(-(\pi )/(2)\right)= 0\\\\


\circ \quad \tan \left(-(\pi )/(2)\right) = -(1)/(0) is not defined


\circ \quad \csc\left(-(\pi )/(2)\right) =-1\\\\


\circ \quad \sec\left(-(\pi )/(2)\right) = \frac {1}{0}\\ is not defined


\circ \quad \cot\left(-(\pi)/(2)\right) =\:0

Explanation:


\text{Values of trig functions for $-(\pi)/(2)$ are: }\\\\


\circ \quad sin\left(-(\pi)/(2)\right) = - sin\left((\pi)/(2)\right) = -1\\\\


\circ \quad \cos \left(-(\pi )/(2)\right)=\cos \left((\pi )/(2)\right) = 0\\\\


\circ \quad \tan \left(-(\pi )/(2)\right) = (sin\left(-(\pi)/(2)\right))/(cos\left(-(\pi)/(2)\right) ) = (-1)/(0)
This is undefined since division by zero is undefined


\circ \quad \csc\left(-(\pi )/(2)\right) = (1)/(sin\left(-(\pi )/(2)\right)) = (1)/(-1) =-1\\\\


\circ \quad \sec\left(-(\pi )/(2)\right) = (1)/(\cos\left(-(\pi )/(2)\right)) = \frac {1}{0}
This is undefined


\circ \quad \cot\left(-(\pi)/(2)\right) = (cos\left(-(\pi )/(2)\right))/(sin\left(-(\pi )/(2)\right))\:=\:(0)/(-1\:)=\:0

User Arafat Khan
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