10.2 Angles of Rotation
Algebra 2
10.2 ANGLES OF ROTATION
Learning Targets:
1. I can draw an angle in standard position.
2. I can find the measure of a positive and negative co-terminal angle.
3. I can find the measure of a reference angle.
4. I can find the values of sine, cosine, and tangent when given the point on the terminal side of an angle in
standard position.
5. I can find the coordinates of a point on the terminal side of an angle in standard position when given the
measure of the angle and length of the terminal side.
An angle is in _______________________________________ when its vertex is at the origin and one ray is on
the positive x-axis.
The ray that is on the positive x-axis is the __________________________________ of the angle.
The other ray is called the _________________________________ of the angle.
Example 1: Draw an angle with the given measure in standard position.
a.
b.
An _______________________________________________ is formed by rotating the terminal side and
keeping the initial side in place.
If the terminal side is rotated counterclockwise, the angle of rotation is ___________________.
If the terminal side is rotated clockwise, the angle of rotation is ___________________.
_______________________________ are angles in standard position with the same terminal side.
Every angle has infinitely many coterminal angles.
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10.2 Angles of Rotation
Algebra 2
Example 2: Find the measures of a positive and a negative angle that are coterminal with the given angle.
a.
b.
For an angle in standard position, the __________________________________ is the positive acute angle
formed by the x-axis and the terminal side of the angle.
Example 3: Find the measure of the reference angle for each given angle.
a.
b.
c.
We can find the values of trigonometric functions for an angle in standard position if you are given a point on
the terminal side of the angle.
Here is a visual representation and the formulas for the trig functions.
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10.2 Angles of Rotation
Algebra 2
Example 4: P (−5,12) is a point on the terminal side of an angle in standard position. Find the exact value of
sin θ , cos θ , and tan θ .
Example 5: An aquarium has a cylindrical tank that rotates at a constant speed about an axis through the center
of the cylinder’s bases. In 1 minute, the tank rotates through an angle of 48°.
a. Draw a picture of the tank to help visualize the problem.
b. How long does it take the tank to make a complete rotation?
c. The tank rotates only during the aquarium’s operating hours. If the aquarium is open from 9:30 A.M. to
6:00 P.M., how many rotations does the tank make in one day?
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