What Is A Radian?

1 radian = the arc length of the radius

of the circle

Radian Angle Measures• based on the ratio of the arc length in a circle to its radius

• still measures the amount of rotation from the initial side to the terminal side.

Radians often use to symbolize the

angle measure.

- Distance around a circle is

circumference. C = 2C = 2rr -Radians uses the unit circle, so r = 1.

This makes the distance

around the circle 22.

III

III IV

Quadrants remain the same, but quadrant angles are now in radians.

In what quadrant would the terminal side of each of the following angles lie?

11 6

-7 4

2 3

-20 3

II I IV III

Finding Coterminal Angles in Radians

In degrees:Add or

subtract any multiple of

360o.

In radians:Add or subtract any

multiple of 2. *Be careful when adding

fractions*

Easiest Way: Add the numbers on

calculator without the then insert the in the

final answer.

Examples:

Find one positive and one negative coterminal angle to . 5

2

Find one positive and one negative coterminal angle to .

6

17

Reference Angle with Radians an acute angle formed by the terminal side of any

angle () and the x-axis( should be a positive angle between 0 – 2)

Quadrant I

=

Quadrant II

Quadrant III

=

Quadrant IV

Find the reference angle () of each given angle (

1) 2/3

2)7/6

3)11/3

4)-4/3

5)-13/5

/3

2) /6

/3

4 /3

5 /5

I HATE Fraction

s!