Question

question 22
find the area of a sector of a circle with radius 18 inches subtended by a central angle of 60°. answer exactly in terms of pi.
square inches
question 23
graph the function and state the amplitude, period, and midline. state the maximum and minimum y values and the corresponding x-values on one period for x ≥ 0.
f(x) = 4 sin(\frac{1}{3}x)

Explanation:

Step1: Write the formula for the area of a sector

The formula for the area of a sector of a circle is \(A=\frac{\theta}{360}\times\pi r^{2}\), where \(\theta\) is the central angle in degrees and \(r\) is the radius of the circle.

Step2: Substitute the given values into the formula

Given \(r = 18\) inches and \(\theta=60^{\circ}\).
Substitute into the formula: \(A=\frac{60}{360}\times\pi\times(18)^{2}\).
First, simplify \(\frac{60}{360}=\frac{1}{6}\).
Then, \((18)^{2}=324\).
So, \(A=\frac{1}{6}\times\pi\times324\).

Step3: Calculate the value

\(A = 54\pi\)

Answer:

\(54\pi\)