October 13, 2011At the end of today, you will be able to:Describe angles and use radian and degree measures.

Warm-up: With a partner brainstorm what you remember about the following:

1. Sketch a positive and a negative angle on two separate graphs.

2. What are complementary and supplementary angles? Give some examples.

3. In which quadrant is the terminal side of a 225° angle?

4. What is 1 radian? Be prepared to teach the class what you remember!

Angles in the coordinate plane• Most of our angles will be in “standard

position” – starting on the positive x-axis.

The initial side of the angle

The terminal side of the angle

The angle measure

Common Angles90° 180°

270° 360°

Positive angles (counterclockwise)Negative angles (clockwise)

The initial side always stays on the x-axis.

Negative Angles

-90°-180°

-270°

-360°

Make a sketch of the following angles:

1. 30° 2. 120° 3. 325°

4. -45° 5. -225° 6. -135°

Coterminal Angles: α + 360k Angles that have the same initial and

terminal sides, but not the same angles.

Example 1: Coterminal angles for 210° α + 360k, k is the number of rotations

When α = 210, 210 + 360(1) =

210 + 360(-1) = Name 2 coterminal angles for 0°.

You try: Determine two coterminal angles (one positive and one negative) for 45° and -36°.

570°-150°

So long, Degrees! Hello, Radians!What is a Radian?

r = the radius of the circle

r

r s = r

θ

One radian is the measure of the angle, θ, when the radius, r, is equal to the length of the arc, s.

Understanding Radians

The unit circle is a circle with a radius of 1.

Two things to recall:It is 360° to go around the

entire circle.Circumference = 2πrSo… 360° = 2π(1) 360° = 2π radians

r = 1

360° = 2π

90° = 2

180° = π

270° = 23

Common Angles

2

90°= 180° = π

270° = 360° = 2π23

Degrees to Radians

180

180

180

When converting from degrees to radians, multiply

Example: Convert 125° to radians.

125 Reduce and leave as a fraction.

3625

Go back to this slide, and rewrite the angles in radians. 1. 30° 2. 120° 3. 325°

4. -45° 5. -225° 6. -135°

6

3665

32

4

45

43

Now let’s go the other way around…Radians to Degrees

180

54

54

Example: Convert to degrees.

180

Multiply

18036

= 144°

Your Turn!!! Convert 34

There’s a shorter way! Ask me.

ClassworkPg. 290 #4, 13, 17, 31, 47, 52

Common Angles in Radians