Lesson 2.1: Angles in Standard Position
Specific Outcome: Demonstrate an understanding of angles in standard position [0o to 360o].
Review:
Trig. Ratios
Pythagorean Theorem
Tan 
opposite
adjacent
Sin 
opposite
hypotenuse
Cos 
adjacent
hypotenuse
c2  a2  b2
hypotenuse
A Cartesian Plane
 Label QI, QII, QIII, and QIV.
 Label the positive x – axis 0o and continue around to 3600.
In geometry, an angle is formed by two rays with a common endpoint. The starting position is called the initial
arm and the final position is called the terminal arm of an angle. If the angle rotation is counterclockwise, then
the angle is positive.
Angles in Standard Position
The diagram in Group A shows the angles in standard position. The angles in Group B are not in standard
position. What are the characteristics of an angle in standard position?
Example 1: Which diagram shows an angle of 70o in standard position?
Example 2: Sketch the rotation angle in standard position and state the quadrant in which the angle terminates.
17o
309o
120o
Note: An angle is said to be an angle in standard position if its vertex is at the origin of the coordinate grid and
its initial arm coincides with the positive x-axis.
Reference Angle
A reference angle is the acute angle (< 90o) formed between the terminal arm and the x-axis. The reference
angle is always positive and measures between 0o and 90o. The right triangle that contains the reference angle
and has one leg on the x-axis is known as the reference triangle.
Example 3: Draw the reference angle for the degree measures listed below.
243o
337o
70o
Example 4: Determine the measure of the rotation angle given the reference angle and the quadrant:
Reference Angle
Quadrant
25°
2
Sketch
Rotation Angle
60°
4
8°
3
39°
1
90°
Between 3 and 4
Example 5: Determine the three angles between 0o and 360o which have the same reference angle as a rotation
angle of 256o.
Example 6: Determine the measure of the three other angles in standard position, 0o < θ < 360o, that have a
reference angle of 65o.
Example 7: Given the point P(2, 3), draw the angle in standard position.
Example 8: Given the point P(-1, 1), draw the angle in standard position.
Practice Questions: Page 83: # 1 – 7, 9