Question

Find the measures of two angles, one positive and one negative, that are coterminal with pi divided by four.

Answer 1

$\frac{ \pi }is the 45 degree angle. the whole circle is 2π. so the positive angle is π/4+2π =\frac{9 \pi }{4}$
 the the negative angle is -(2π-π/4)= -\frac{7 \pi }{4}  

Answer 2

Answer:  The positive co-terminal angle is $\dfrac{9\pi}{4}.$ and the negative co-terminal angle is $-\dfrac{7\pi}{4}.$

Step-by-step explanation:  We are to find the measures of the two angles, one positive and one negative, that are co-terminal with pi divided by four.

We know that

any two co-terminal angles differ from each other by an integral multiple of $2\pi.$

So, to find the positive co-terminal angle, we will add $2\pi$ to $\dfrac[\pi}{4}$ and to find the negative co-terminal angle, we will subtract $2\pi$ from $\dfrac[\pi}{4}$.

Therefore, the required positive co-terminal angle is given by

$C_p=\dfrac{\pi}{4}+2\pi=\dfrac{\pi+8\pi}{4}=\dfrac{9\pi}{4}.$

And, the required negative co-terminal angle is given by

$C_n=\dfrac{\pi}{4}-2\pi=\dfrac{\pi-8\pi}{4}=-\dfrac{7\pi}{4}.$

Thus, the positive co-terminal angle is $\dfrac{9\pi}{4}.$ and the negative co-terminal angle is $-\dfrac{7\pi}{4}.$