Question

question 1
choose all angle measures below that are coterminal to 240°. (there is more than one answer)
240 degrees
$\frac{2pi}{3}$
-60 degrees
600 degrees
-240 degrees
-120 degrees
-$\frac{2pi}{3}$
120 degrees

Explanation:

Step1: Recall coterminal - angle formula

Coterminal angles to an angle $\theta$ are given by $\theta\pm360^{\circ}n$ (in degrees) or $\theta\pm 2\pi n$ (in radians), where $n$ is an integer.

Step2: Check each option

• For $\theta = 240^{\circ}$:
• Option 1: $240^{\circ}$ is coterminal with itself ($n = 0$), since $240^{\circ}=240^{\circ}+360^{\circ}\times0$.
• Option 2: $\frac{2\pi}{3}$ radians. Convert $\frac{2\pi}{3}$ to degrees: $\frac{2\pi}{3}\times\frac{180^{\circ}}{\pi}=120^{\circ}$, and $120^{\circ}$ is not coterminal with $240^{\circ}$.
• Option 3: $- 60^{\circ}$ is not coterminal with $240^{\circ}$ because $240^{\circ}-360^{\circ}= - 120^{\circ}

eq - 60^{\circ}$.

• Option 4: $600^{\circ}=240^{\circ}+360^{\circ}\times1$, so $600^{\circ}$ is coterminal with $240^{\circ}$.
• Option 5: $-240^{\circ}$ is not coterminal with $240^{\circ}$ as $240^{\circ}-360^{\circ}

eq - 240^{\circ}$.

• Option 6: $-120^{\circ}$ is not coterminal with $240^{\circ}$.
• Option 7: $-\frac{2\pi}{3}$ radians. Convert $-\frac{2\pi}{3}$ to degrees: $-\frac{2\pi}{3}\times\frac{180^{\circ}}{\pi}=-120^{\circ}$, not coterminal with $240^{\circ}$.
• Option 8: $120^{\circ}$ is not coterminal with $240^{\circ}$.

Answer:

240 degrees, 600 degrees