Back to Trig Quick Review: Convert 200 degrees to radians

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Presentation transcript:

Back to Trig Quick Review: Convert 200 degrees to radians Convert 2∏/3 to degrees Find the arc length that is intercepted by an angle of 2 radians and a radius of 14cm. Find the radius of a circle that will intercept an arc of 4 meters with a central angle of 30o

New Uses for Radian Measure, Etc Linear Speed Formula: Linear Speed = (arc length)/time V = s/t Example: The second hand of a clock is 10.2 cm long. Find the linear speed of the tip of the second hand as it passes around the clock face.

New Uses for Radian Measure, Etc Angular Speed Formula: Angular Speed = (central angle)/time w = Θ/t Example: The blades of a wind turbine are 116 ft long. The propeller rotates at a rate of 15 revolutions per minute. Find the angular speed of the propeller in radians per minute Find the linear speed of the tips of the blades

New Uses for Radian Measure, Etc Area of a Sector of a Circle Formula: Area = ½ r2 Θ The angle must be in radians! Example: A sprinkler on a golf course sprays 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.

New Uses for Radian Measure, Etc RPM A tractor trailer and an SUV are traveling next to each other on the Long Island Expressway at approximately 65mph. The tractor trailer’s tires have a diameter of 40 inches. The SUV’s tires have a diameter of 29 inches Estimate the revolutions per minute of the tires for each vehicle Assuming a tire has a life of 27 million revolutions, how far will each vehicle be able to travel on one set of tires. If the tractor trailer tires are $350 each and the SUV tires are $279 each, which tire is the better buy?