$\"\"$

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a.

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Arc( $\"\"$ ) length of the circle is $\"\"$ , where $\"\"$ .

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When $\"\"$ and $\"\"$ , the radius of the circle is $\"\"$ .

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Consider $\"\"$ .

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Substitue $\"\"$ and $\"\"$ in above equation.

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$\"\"$

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Now the trigonometric equation is $\"\"$ , where $\"\"$ .

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Let the functions are $\"\"$ and $\"\"$ .

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Draw a coordinate plane.

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Graph the two functions $\"\"$ and $\"\"$ on the interval $\"\"$ in same window.

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Graph :

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$\"\"$

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Observe the above graph :

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The two functions intersects at $\"\"$ on the interval $\"\"$ .

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Thus, $\"\"$ .

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The value of $\"\"$ is $\"\"$ radians.

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$\"\"$

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b.

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Find the angle $\"\"$ in radian measure.

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Area of the shaded region is $\"\"$ .

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Consider $\"\"$ .

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Substitue $\"\"$ and $\"\"$ in above equation.

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$\"\"$

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Now the trigonometric equation is $\"\"$ .

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Let the functions are $\"\"$ and $\"\"$ .

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Draw a coordinate plane.

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Graph the two functions $\"\"$ and $\"\"$ on the interval $\"\"$ in same window.

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Graph :

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$\"\"$

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Observe the above graph :

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The two functions intersects at $\"\"$ on the interval $\"\"$ .

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When the area is 36 square inches and the radius is 5 inches, then the measure of $\"\"$ is $\"\"$ radians.

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$\"\"$

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a. The value of $\"\"$ is $\"\"$ radians.

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b. When the area is 36 square inches and the radius is 5 inches, then the measure of $\"\"$ is $\"\"$ radians.