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Degrees and radians
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Angles and their measures
The measure of an angle describes the amount and direction of rotation necessary to move from the initial side to the terminal side of the angle.
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Positive or negative?
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How many degrees are in half of a rotation?
The most common angular unit of measure is a degree (◦). There are 360 degrees in a circle. How many degrees are in half of a rotation? How many degrees are in quarter of a rotation?
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Radians 𝜃= 𝑠 𝑟 What is the value of θ for the entire circle?
What is the value of θ for a half a rotation? What is the value of θ for a quarter rotation?
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Convert from degrees to radians
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Coterminal angles
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Find and draw coterminal angles
Find and draw one positive and one negative angle coterminal with the given angle. 45° − 𝜋 3 −30° 3𝜋 4
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Arc Length 𝑠=𝑟𝜃
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Find the arc length of the intercepted arc in each circle with the given central angle measure and radius. Round to the nearest tenth. 𝜋 4 , 𝑟=5 𝑐𝑚 60°, 𝑟=2𝑖𝑛 2𝜋 3 , 𝑟=2𝑚 135°, r=0.5 ft
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Linear and Angular Speed
Recall that the formula for velocity is: If we want to know angular velocity, then the formula would be: 𝜔= 𝜃 𝑡 Where 𝜃 is the angular distance covered.
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Real World Example A bicycle messenger rides the bicycle shown.
During one delivery, the tires rotate at a rate of 140 revolutions per minute. Find the angular speed of the tire in radians per minute. On part of the trip to the next delivery, the tire turns at a constant rate of 2.5 revolutions per second. Find the linear speed of the tire in miles per hour.
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