Download 10.2A Angles of Rotation

10.2A Angles of Rotation
Objective:
F.TF.2: Explain how the unit circle in the coordinate plane enables the extension of
trigonometric functions to all real numbers, interpreted as radian measures of angles
traversed counterclockwise around the unit circle.
For the Board: You will be able to draw angles in standard position and determine the values of the
trigonometric functions for an angle in standard position.
Anticipatory Set:
In the previous section we worked with acute angles of a right triangle.
In this section we will investigate angles in the coordinate plane.
An angle is in standard position when its vertex is at the origin and
one ray is on the positive x-axis.
The initial side of the angle is the ray on the x-axis and the other ray
is the terminal side of the angle.
Angle measure is then based on the degree of rotation.
90°
Terminal side
180°
An angle of rotation is formed by rotating the terminal side and keeping
the initial side in place.
Rotation can be either clockwise or counterclockwise.
Counterclockwise is considered the positive rotation direction.
Clockwise is considered the negative rotation direction.
270°
Positive Rotation
Negative Rotation
90°
-270°
Terminal side
180°
Initial side
+ degree
Initial side
0°
- 180°
Terminal side
270°
Instruction:
Open the book to page 700 and read example 1.
Example: Draw an angle with the given measure in standard position.
a. 320°
b. -110°
Initial side
- degree
- 90°
c. 990°
0°
0°
White Board Activity:
Practice: Draw an angle with the given measure in standard position.
a. 210°
b. 1020°
c. -300°
Coterminal angles are angles in standard position with the same terminal side.
Example: Angles measuring 120°, -240°, and 480° are coterminal.
There are infinitely many coterminal angles.
To find the measure of an angle which is coterminal to a given angle, add or subtract 360°.
Open the book to page 701 and read example 2.
Example: Find the measures of a positive angle and a negative angle that are coterminal with
each given angle.
a. θ = 65°
b. θ = 410°
65° + 360° = 425
410° + 360° = 770°
65° – 360° = -295°
410° – 360° = 50°
White Board Activity:
Practice: Find the measures of a positive angle and a negative angle, that are coterminal with
each given angle.
a. θ = 88°
b. θ = 500°
c. θ = -120°
448°, -272°
140°, -220°
-480°, 240°
Assessment:
Question student pairs:
Independent Practice:
Text: pg. 703 prob. 2 – 9, 26 – 33, 50.
For a Grade:
Text: pg. 703 prob. 26, 30, 50.