5.1 angles and radian measure
DESCRIPTION
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. - PowerPoint PPT PresentationTRANSCRIPT
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)