Question

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

HELP PLZZZZZ

Answer 1

Answer: The positive co-terminal angle is
`(9\pi)/(4).` and the negative co-terminal angle is
`-(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
`\frac[\pi}{4}` and to find the negative co-terminal angle, we will subtract
`2\pi` from
`\frac[\pi}{4}`.

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

`C_p=(\pi)/(4)+2\pi=(\pi+8\pi)/(4)=(9\pi)/(4).`

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

`C_n=(\pi)/(4)-2\pi=(\pi-8\pi)/(4)=-(7\pi)/(4).`

Thus, the positive co-terminal angle is
`(9\pi)/(4).` and the negative co-terminal angle is
`-(7\pi)/(4).`

Answer 2

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