Angles and Radian Measure in Mathematics
Explore the concept of angles and radian measures in mathematics. Learn about angles, quadrants, measuring angles using degrees, and converting between degrees and radians. Discover how to calculate radian measures and degrees in practical examples.
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Presentation Transcript
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 http://3.bp.blogspot.com/_msFND1beseI/TLoi1SUfIJI/AAAAAAAAABs/rxb1FLU6PTk/s200/quad..jpg 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. Radian - en.svg
Ex #1: RADIAN MEASURE = ? ??? ????? ?????? ? A central angel, , ina circle of radius 12 feet intercepts an arc of length 42 feet. What is the radian measure of ?
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. Radian - en.svg
Plus just a little bit more!
Radians and Degrees If = ? REMEMBER: Circumference = 2 r ??? ????? ?????? what is the angle of the entire circle? ?
CONVERSION Degrees Radians ? Degrees * 180 Radians Degrees Radians * 180 ?
Ex #2-3 CONVERT TO RADIANS: 30 90 135 CONVERT TO DEGREES: 3 radians 5? 3 radians 1 radian ?
Drawing Angles in Standard Position Ex #4: Draw the following angles ? =? 4 = 4 ? = 3? 4 ? =9? 4 5?
Drawing Angles in Standard Position Ex #4: Draw the following angles ? = ? 4 = 4 ? = 7? 4 ? =13? 4 3?
FINDING COTERMINAL ANGLES http://www.analyzemath.com/Angle/coterminal_1.gif 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)
