Degrees and radians

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.

Positive or negative?

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?

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?

Convert from degrees to radians

Coterminal angles

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

Arc Length 𝑠=𝑟𝜃

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

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.

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.