Download Trig Readiness 3 – Angle Standard Position

Math 150 – Fall 2015
Trig Readiness 2
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Trig Readiness 3 – Angle Standard Position
Definition.
• Given two rays sharing a common endpoint, the amount of rotation
about this common endpoint to move from one ray to the other is called an angle.
• The common endpoint is called the vertex.
• The side where the rotation begins is called the initial side or the initial position, and the final side is called the terminal side.
• If the rotation is counter-clockwise, then the angle is positive. If the rotation is
clockwise, then the angle is negative.
Definition. An angle is in standard position if it has its vertex at the origin and its
initial side along the positive x axis.
Definition. If an angle is in standard position, the reference angle is the smallest
angle between the terminal side and the x-axis.
Figure 1: Reference Angle
Math 150 – Fall 2015
Trig Readiness 2
2 of 2
Suppose a circle is centered at the original and an angle is in standard position. We will
use the x and y values of the point where the terminating side of the angle intersects
the circle to define the trig functions. Where the angle intersects the x-axis will form
a reference triangle seen below. We will use our standard triangles (see Trig 2) to
label the side lengths of the reference triangle. The hypoteneuse is always positive, but
the legs will be positive or negative depending on the quadrant.
For the quiz this week, you should be able to answer a question like the following. You
can also study with using Learning Catalytics with session id 67000814 (only study
#1-6). The Learning Catalytics only asks for reference angles, but you need to know
the whole reference triangle.
Example. For the following angles, sketch the reference triangle in the coordinate
plane. Then label the reference angle and the three sides of the reference triangle. The
legs of the reference triangle should be positive or negative depending on the quadrant.
Reference Triangle
π
4
:
3π
2 :
5π
3 :
5π
6 :
5π
4 :
11π
6 :
8π
3 :
Reference Angle
x
y
r