Question

In the circle shown below, ∠BAC is a central angle, and r is the length of AB.

The area of the shaded sector is equal to 1/2r^2θ. Which of the following must be true about the value of θ?

θ= the measure of ∠BAC in degrees.

θ= the measure of ∠BAC in radians

θ= the difference between 2π and the measure of ∠BAC in radians

θ= the difference between 360 and the measure of ∠BAC in degrees

Answer 1

Ф = the measure of ∠BAC in radians

Explanation:

∵ ∠BAC is a central angle

∴ The are of the sector will depended on the length of the radius r and the measure of the central angle Ф

If the measure of Ф in degrees

∴ The area of the sector = Ф°/360° (π r²)

If the measure of Ф in radians

∴ The area of the sector = 1/2 r² Ф

When to change from degree to radian you do that

Ф radian = Ф°/180 × π

∴ Ф/360 π r² = 1/2 (Ф/180 π) r² ⇒ ∵ underline is Ф radian

∴ Area sector = 1/2 r² Ф ⇒ Ф in radians