Answer: The required measures of two angles one positive and negative that are co-terminal with [tex]\dfrac{\pi}{2}[/tex] are [tex]-\dfrac{3\pi}{2}[/tex] and [tex]\dfrac{5\pi}{2}.[/tex]
Step-by-step explanation: We are given to find measures of two angles one positive and negative that are co-terminal with [tex]\dfrac{\pi}{2}.[/tex]
Let x and y represents the positive and negative co-terminal angles respectively.
We know that
the measures of any two co-terminal angles differ from each other by a multiple of [tex]2\pi.[/tex]
So, the values of x and y can be found as follows :
[tex]x=\dfrac{\pi}{2}-2\pi=-\dfrac{3\pi}{4},\\\\\\y=\dfrac{\pi}{2}+2\pi=\dfrac{5\pi}{2}.[/tex]
Thus, the required measures of two angles one positive and negative that are co-terminal with [tex]\dfrac{\pi}{2}[/tex] are [tex]-\dfrac{3\pi}{2}[/tex] and [tex]\dfrac{5\pi}{2}.[/tex]
