Question

find the area of this sector if r = 2 and \\(\theta = \frac{17\pi}{36}\\) radians. ?\\(\pi\\) sq units

Explanation:

Step1: Recall the sector area formula

The formula for the area of a sector when the central angle \(\theta\) is in radians is \(A=\frac{1}{2}r^{2}\theta\).

Step2: Substitute the given values

We know that \(r = 2\) and \(\theta=\frac{17\pi}{36}\). Substitute these values into the formula:
\(A=\frac{1}{2}\times(2)^{2}\times\frac{17\pi}{36}\)
First, calculate \((2)^{2}=4\). Then, \(\frac{1}{2}\times4 = 2\). So now we have \(A = 2\times\frac{17\pi}{36}\).

Step3: Simplify the expression

Simplify \(2\times\frac{17\pi}{36}\). The 2 and 36 can be simplified: \(\frac{2\times17\pi}{36}=\frac{17\pi}{18}\).

Answer:

\(\frac{17}{18}\)