Question

for #7 - 9, find the radian measure of the angle.

1. 1/8 rotation, counterclockwise
2. 7/6 rotation, clockwise

Explanation:

Step1: Recall the formula for angle in radians

One full rotation is \(2\pi\) radians.

Step2: Calculate for \(\frac{1}{8}\) counter - clockwise rotation

Multiply the fraction of rotation by \(2\pi\). So, \(\frac{1}{8}\times2\pi=\frac{\pi}{4}\) radians.

Step3: Calculate for \(\frac{7}{6}\) clockwise rotation

Since it's clockwise, the angle is negative. Multiply \(\frac{7}{6}\) by \(2\pi\) and add the negative sign. So, \(-\frac{7}{6}\times2\pi=-\frac{7\pi}{3}\) radians.

Answer:

For \(\frac{1}{8}\) counter - clockwise rotation: \(\frac{\pi}{4}\) radians. For \(\frac{7}{6}\) clockwise rotation: \(-\frac{7\pi}{3}\) radians.