Question

the measure of an angle in standard position is given. find two positive angles and two negative angles that are coterminal with the given angle. (enter your answers as a comma - separated list.) 225°

Explanation:

Step1: Recall coterminal - angle formula

Coterminal angles of an angle $\theta$ are given by $\theta + 360^{\circ}n$, where $n$ is an integer.

Step2: Find positive coterminal angles

For $n = 1$, $\theta_1=225^{\circ}+360^{\circ}\times1 = 585^{\circ}$.
For $n = 2$, $\theta_2=225^{\circ}+360^{\circ}\times2=945^{\circ}$.

Step3: Find negative coterminal angles

For $n=-1$, $\theta_3=225^{\circ}+360^{\circ}\times(-1)=225^{\circ} - 360^{\circ}=-135^{\circ}$.
For $n = - 2$, $\theta_4=225^{\circ}+360^{\circ}\times(-2)=225^{\circ}-720^{\circ}=-495^{\circ}$.

Answer:

$585^{\circ},945^{\circ},-135^{\circ},-495^{\circ}$