Question

Look at the radian measure for every 30 degrees and 45 degrees in the Unit Circle. Explain how finding the exact measure in quadrant one can help you determine the remaining exact radian measures.

Answer 1

Google radian measures on the unit circle for lots of images of completed unit circles with these radian measurements. But the core idea is that if you can find the 30° and 45° radian measures (π/6 and π/4 respectively) to move to the corresponding angle in quadrant 2, you'd just need to add π/2 (90°) to that value, to find the values in quadrant 3 add π (180°), quadrant 4 add 3π/4 or you could also just minus π/2 to move 90° in the opposite direction. Say I wanted to find the 45° angle in quadrant 3, measured from the 0° line on the unit circle, in radians. I could say I know 45° is π/4 in quadrant 1, so to move it to quadrant 3, I need to add π or 180° to it. π/4 + π = π/4 + 4π/4 = 5π/4 which is the angle we need in radians.