Question

Why are the 45-degree angles in the unit circle considered π/4 instead of π/8?

A) They bisect the quadrant
B) They divide the whole circle into eighths
C) They form right angles with the x-axis
D) They are double the measure of 22.5-degree angles

Why are the 30-degree angles in the unit circle considered π/6 instead of π/12?
A) They bisect the quadrant
B) They divide the circle into 12 parts
C) They are complementary to 60-degree angles
D) They are triple the measure of 10-degree angles

Answer 1

The 45-degree angles are considered π/4 because they bisect the quadrant, and the 30-degree angles are considered π/6 because they divide the circle into 12 equal parts.

Step-by-step explanation:

The 45-degree angles in the unit circle are considered π/4 because they bisect the quadrant, meaning they divide the quadrant into two equal parts, each measuring 45 degrees. Since there are four quadrants in a circle, this means the entire circle is divided into 8 parts, with each part being a 45-degree angle. The radian measure of each part is therefore π/4.

The 30-degree angles in the unit circle are considered π/6 because they divide the circle into 12 equal parts, with three of these 30-degree angles making up a quadrant. Each quadrant has 90 degrees, and dividing 90 degrees by three gives you the 30-degree angle measure. Moreover, since each 30-degree angle divides the circle into 12 parts, the radian measure is π/6.