7.1 Radians and Arc Length.notebook

1

April 08, 2016

Happy Friday!I will convert radians to degrees and degrees to radians on guided notes and classwork.

OUTCOMES for today:

1. Please pick up: 

       ‐calculator

‐warm up

2. Complete the warm up.

7.1 Radians and Arc Length.notebook

2

April 08, 2016

7.1 Radians and Arc Length.notebook

3

April 08, 2016

Outcomes: I will convert from radians to degrees and degrees to radians.

I will determine arc length.

7.1 Radians and Arc Length.notebook

4

April 08, 2016

7.1 Notes: Radians and Degrees

An angle is a measure of rotation usually measured in degrees from the initial side to the terminal side.

An angle is formed from two rays joined end to end.

An angle in standard position is an angle where the initial side is the x­axis.

7.1 Radians and Arc Length.notebook

5

April 08, 2016

For example:

To go from the standard position back to the original standard position, the angle would have to be:

If more than 360o, rewrite the angle as one less than 360o.For example:

420o 900o 720o

7.1 Radians and Arc Length.notebook

6

April 08, 2016

Positive angles: Negative angles:

If given a negative angle, rewrite as a positive angle.

For example:

­78o

­250o

­840o

7.1 Radians and Arc Length.notebook

7

April 08, 2016

Angles can also be measured in radians.

Given a circle with a radius of 1. The radian measure is the angle that describes the distance around the circle.

For example:

Circumference = 2πr

7.1 Radians and Arc Length.notebook

8

April 08, 2016

Therefore 2π radians = 360o.

If 360o = 2π radians, find 90o, 180o and 270o.

7.1 Radians and Arc Length.notebook

9

April 08, 2016

Radians to Degrees:1. (Radian)(180/π) = degrees2. Rewrite the degree as a positive number less

than 360o

For example: Convert to degrees.

3π/2

­14π/5

33π/8

­8π/3

7.1 Radians and Arc Length.notebook

10

April 08, 2016

Degrees to Radians:1. Rewrite the degree as a positive number less

than 360o

2. (Degree)(π/180) = radians

For example: Convert to radians.

255o ­150o ­754o

7.1 Radians and Arc Length.notebook

11

April 08, 2016

Classwork#1­16