Question

find the measure of the angle θ, given that θ is an integer when measured in radians
what is the radian measure of the angle? 3

Explanation:

Step1: Analyze the angle position

The angle is in the second - quadrant. We know that the full circle is \(2\pi\approx6.28\) radians and a straight line (semicircle) is \(\pi\approx3.14\) radians.

Step2: Determine the integer value

Since \(\theta\) is an integer and \(\pi\approx3.14\), and the angle is less than \(\pi\) (as it is in the second - quadrant but not reaching the negative \(x\) - axis which is \(\pi\) radians). The closest integer to a value less than \(\pi\) (but greater than \(\frac{\pi}{2}\approx1.57\)) is \(3\).

Answer:

\(3\)