Question

jayson notices that logo a is divided into 6 equals sections where \\( \overline { c b } \\) is the diameter. \\( \angle b o z \\) is displayed in grey.
which measurement represents \\( \angle b o z \\) in radians?
a \\( \frac { \pi } { 6 } \\)
b \\( \frac { \pi } { 3 } \\)
c \\( \frac { 2 \pi } { 3 } \\)
d \\( \frac { 3 \pi } { 6 } \\)

Explanation:

Step1: Recall the total angle in a circle

The total angle in a circle is \(2\pi\) radians.

Step2: Calculate the angle per section

Since the circle (Logo A) is divided into 6 equal sections, the angle per section is \(\frac{2\pi}{6}=\frac{\pi}{3}\) radians. But wait, we can also think in terms of the relationship between central angles. If we consider that \(\angle BOZ\) is one - sixth of the semi - circle (because \(CB\) is a diameter, and the semi - circle has an angle of \(\pi\) radians). The measure of \(\angle BOZ=\frac{\pi}{3}\) radians.

Answer:

B. \(\frac{\pi}{3}\)