Convert each radian measure to degrees π/3 7π/4 11π/6 -π/6 7π/10

Section 3.2 Applications of Radian Measure

Example: Finding Arc Length A circle has radius 18.2 cm. Find the length of the arc intercepted by a central angle having each of the following measures. a) b) 144

Example: Finding Arc Length continued a) r = 18.2 cm and  = b) convert 144 to radians

Example: Finding a Length A rope is being wound around a drum with radius .8725 ft. How much rope will be wound around the drum it the drum is rotated through an angle of 39.72? Convert 39.72 to radian measure.

FINDING AN ANGLE MEASURE USING s = rθ Two gears are adjusted so that the smaller gear drives the larger one. If the smaller gear rotates through an angle of 225°, through how many degrees will the larger gear rotate? First find the radian measure of the angle, and then find the arc length on the smaller gear that determines the motion of the larger gear.

The larger gear rotates through an angle of 117°. The arc length on the smaller gear is An arc with this length on the larger gear corresponds to an angle measure θ: Convert θ to degrees: The larger gear rotates through an angle of 117°.

Area of a Sector of a Circle A sector of a circle is a portion of the interior of a circle intercepted by a central angle. Think of it as a “ piece of pie.”

Area of a Sector The area A of a sector of a circle of radius r and central angle θ is given by

Find the area of the sector-shaped field shown in the figure. FINDING THE AREA OF A SECTOR-SHAPED FIELD Find the area of the sector-shaped field shown in the figure. Convert 15° to radians.

Area of a Fairway 120o = how many radians? 70 ft A sprinkler on a golf course fairway is set to spray water over a distance of 70 feet and rotates through an angle of 120 degrees. Find the area of the fairway watered by the sprinkler. 120o = how many radians? 70 ft

Arc Length and Area of a Sector 1. Find the arc length, s, and area, A, of the sector of a circle of radius 7 cm. and sector angle 2 radians. Solution: s = r where is in radians S = (7) (2) S = 14 cm

Arc Length and Area of a Sector 4 cm A l 2. Find the arc length, l, and area, A, of the sector shown.