Chapter 4

Trigonometry Day 1

( Covers Topics in 4.1)

5 Notecards

Initial side

Terminal side

Positive Angle (counterclockwise)

Negative Angle (clockwise)

Angles

For example, on the coordinate plane:

0˚ is the positive x-axis

130˚

-70˚

90˚

180˚

270˚

360˚

A radian is the measure of the central angle that intercepts an arc c equal in length to the radius of the circle:

1 radian

2 radians

3 radians

4 radians

5 radians

6 radians

The radius of the circle fits around the circumference 6.28 times ( 2π ).

What is a Radian?

Radian

Quadrants:

IIIIII IV

Coterminal Angles

Two angles are coterminal if they have the same initial side and terminal side

** To find coterminal angles, either add or subtract 2π or 360°.

Coterminal Angles

Ex1: Find a positive and a negative coterminal angle for 125°.

Ex 2: Find a positive and negative coterminal angle for 5

4

54

2 54

84

13

454

2 54

84

3

4

125+360=485°

125-360=-235 °

Converting between Radians and Degrees

from Degrees to Radians

Multiply by

from Radians to Degrees

Multiply by

180

180

Converting between Radians and Degrees

Ex1: Change 270° into radians

Ex 2: Change 135 ° into radians

Ex 3: Change into degrees

Ex 4: Change into degrees

23

54

3π/2

3π/4

120˚

225˚

Arc Length

For a circle of radius r, a central angle ( in radians) intercepts an arc of length s:

S = r

( is in radians) r

S

Arc Length

Ex 1: What is the arc length of a sector if r=4 inches and =240º

(Remember- you must convert to radians first)

Sketching Angles

You will now do a plate activity with your teacher .

Sketching an angle

Sketch a graph of the following angles:

1. 273º

2.

3.1000 º

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