Question

sketch an angle in standard position that results from the given rotation. find the radian measure of the angle.

1. \\( \frac { 1 } { 4 } \\) rotation, counterclockwise
2. \\( \frac { 1 } { 2 } \\) rotation, counterclockwise
3. \\( \frac { 3 } { 4 } \\) rotation, counterclockwise
4. 1 rotation, counterclockwise
5. \\( \frac { 1 } { 4 } \\) rotation, clockwise
6. \\( \frac { 1 } { 2 } \\) rotation, clockwise
7. \\( \frac { 1 } { 6 } \\) rotation, clockwise
8. \\( \frac { 1 } { 8 } \\) rotation, counterclockwise

Explanation:

Step1: Recall the formula for radian measure of an angle

The formula for the radian measure of an angle \(\theta\) in terms of rotation \(n\) is \(\theta = 2\pi n\). For counter - clockwise rotation, \(n>0\) and for clockwise rotation \(n < 0\).

Step2: Calculate the radian measure for \(\frac{3}{4}\) counter - clockwise rotation

Here, \(n=\frac{3}{4}\) (since it is counter - clockwise). Substitute \(n = \frac{3}{4}\) into the formula \(\theta=2\pi n\).

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Answer:

The radian measure of the angle for \(\frac{3}{4}\) counter - clockwise rotation is \(\frac{3\pi}{2}\) radians.