Question

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

with work shown please.

Answer 1

`\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`