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Degrees and radians.

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Presentation on theme: "Degrees and radians."— Presentation transcript:

1 Degrees and radians

2 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.

3 Positive or negative?

4 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?

5 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?

6 Convert from degrees to radians

7 Coterminal angles

8 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

9 Arc Length 𝑠=𝑟𝜃

10 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

11 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.

12 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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