Download Angles in Standard Position

LESSON 1: ANGLES IN STANDARD POSITION
Learning Outcome: Learn to:


Sketch an angle from 0˚ to 360˚ in standard position and determine its reference
angle
Determine the quadrant in which an angle in standard position terminates
Angles occur in many everyday situations. With a partner, try to name as many occupations that
need to use angles.
In geometry, an angle is formed by two rays with a common endpoint. The positive x-axis is
called the initial arm, and the arm that measures out the angle is called the terminal arm.
Terminal Arm
θ
Initial Arm
If the angle of rotation is counterclockwise, then the angle is positive.
Standard Position
Draw an angle of 45˚ in standard position:
Not in Standard
Position
Using the coordinate axes grid paper, use a protractor to draw each angle in standard position. In
which quadrant does the terminal arm lie?
a. 75˚
b. 110˚
c. 240˚
d. 330˚
With a partner, create a definition for an angle in standard position.
Create a coordinate plane then label its quadrants and the angles that encompass each quadrant.
Reference Angles: the acute angle whose vertex is the origin and whose arms are the terminal
arm of the angle and the x-axis.
Reference angles always measure positive and between 0˚-90˚
Using a protractor and a coordinate grid draw:
a. an angle of 30˚, what angle does the terminal arm make with the x-axis?
b. an angle of 150˚, what angle does the terminal arm make with the x-axis?
c. an angle of 210˚, what angle does the terminal arm make with the x-axis?
d. an angle of 330˚, what angle does the terminal arm make with the x-axis?
With a partner, use a diagram to illustrate how we can find the reference angle in each quadrant.
Determine the reference angle for each angle. Sketch θ in standard position and label the
reference angle 𝜃𝑅 .
a. θ = 140˚
b. θ = 320˚
Co-terminal angles: angles that have the same terminal arm
Counterclockwise (+): positive angles rotate counter-clockwise
Clockwise (-): negative angles rotate clockwise
Examples: Sketch 405˚, 540˚, 690˚, -210˚, 920˚, -370˚
Principle Angle: smallest positive co-terminal angle (between 0˚ and 360˚)
Ex. Find one positive and one negative angle co-terminal with each. Also find the principle
angle and reference angle for each.
a. 108˚
b. -70˚
c. 587˚
Assignment: pg. 83-87 #1-7