Download 17-1 Angles of Rotation and Radian Measure

17-1 Angles of Rotation and
Radian Measure
Extend the domain of trigonometric functions
using the unit circle
1. Understand radian measure of an angle as
the length of the arc on the unit circle
subtended by the angle
Quadrants of a Coordinate Plane
The coordinate plane is divided into 4 parts.
• Label each part as a Quadrant I, Quadrant II,
Quadrant III and Quadrant IV
counterclockwise starting from the positive
part.
Quadrant II
Quadrant I
Quadrant III
Quadrant IV
Angles in standard position
• An angle is in standard
position when the vertex is
at the origin and one ray is
on the positive x-axis. The
ray on the x-axis is the initial
side and the other ray is the
terminal side of the angle.
• The measure of an angle is
positive when the rotation
from the initial side to the
terminal side is in the
counteclockwise direction.
The measure is negative when
the rotation is clockwise.
• Two angles in standard position are
coterminal angles if they have the same
terminal side.
• For example : angles that have measures 135o
and – 225o are coterminal.
• The angles drawn can be more than 360o if
the angles is rotated more than 1 revolution.
1.
Draw an angle of rotation of
310o. In what quadrant is
the terminal side of the
angle?
1.
Draw a positive coterminal
angle. What is the angle
measure of your angle?
2.
Draw a negative coterminal
angle. What is the angle
measure of your angle?
Understanding Radian Measure
• 1 radian is the angle that
intercepts an arc of length 1 on
a unit circle, as shown.
• 360o = 2π radian
• Converting Degrees to Radians
• Multiply the number of degrees by
• π radians /180o
• Converting Radians to Degrees
• Multiply the number of radians by
• 180o/ π radians
Assignment
• Download the PDF Document from
• Chungmachs.weebly.com
• A3 radians