Arcs & Sectors

Length of Arcs & Area of Sectors

Let's Review Degrees, Radians, Arc Lengths and Sector Areas

Converting Radians & Degrees

• Degrees x  $\frac{\pi}{180}$  = Radians

• Radians x  $\frac{180}{\pi}$  = Degrees

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 $\frac{\pi}{9}$  Convert the radian to degrees.

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Convert 240 degrees to radians. Write pi as pi in your answer.

Lengths of Arcs

• Formula --> $s=r\theta$  

•  $\theta$  must be in radian form

• OR use other form of equation shown to the right ------------->

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Find the length of arc XY. Simplify.

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Determine the length of the arc, given the radius and central angle. Simplify.

Area of Sectors

• Formula --> $A=\frac{1}{2}r^2\theta$  

•  $\theta$  must be in radian form

• OR use other formula to right -->

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Find the area of a sector if the central angle measures 30° radians and the radius of the circle is 11 cm. Simplify.

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Determine the area of the sector, given the radius and the central angle.