5.1 Angles and Radian Measure

ANGLES

• Ray – only one endpoint• Angle – formed by two rays with a common endpoint• Vertex – the common endpoint of an angle’s initial

and terminal sides.

-Vertex @ origin-Initial side lies along positive x-axis

QUADRANTS

When in standard position, an angle’s terminal side lies in a quadrant.

Quadrantal Angle

Not in a quadrant. Terminal side is on either the x- or y-axis.

MEASURING ANGLES USING DEGREES

• Acute

• Right

• Obtuse

• Straight

MEASURING ANGLES IN RADIANS

• One radian is the measure of the central angle of a circle that intercepts an arc equal in

length to the radius of the circle.

Ex #1: RADIAN MEASURE• ϴ =

• A central angel, ϴ, ina circle of radius 12 feet intercepts an arc of length 42 feet. What is

the radian measure of ϴ?

MEASURING ANGLES IN RADIANS

• One radian is the measure of the central angle of a circle that intercepts an arc equal in

length to the radius of the circle.

Plus just a little bit more!

Radians and DegreesIf ϴ = what is the angle of the entire circle? REMEMBER: Circumference = 2πr

CONVERSION

• Degrees RadiansDegrees * • Radians DegreesRadians *

Ex #2-3

• CONVERT TO RADIANS:

• CONVERT TO DEGREES:• radians• radians• radian

Drawing Angles in Standard Position

• Ex #4: Draw the following angles

Drawing Angles in Standard Position

• Ex #4: Draw the following angles

UNIT CIRCLE

FINDING COTERMINAL ANGLES

NOTICE: YOUR BOOK ASKS FOR POSITIVE ANGLES LESS THAN 360

HOMEWORK

•Pg. 480 #1-55 odd+ pg. 476 Checkpoint #5(you’ll need to read Example 5 in

order to do the checkpoint)