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. 90° 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 Terminal side is the terminal side of the angle. 180° 0° Initial side Angle measure is then based on the degree of rotation.

An angle of rotation is formed by rotating the terminal side and keeping the initial side in place. 270° Rotation can be either clockwise or counterclockwise. Counterclockwise is considered the positive rotation direction. Clockwise is considered the negative rotation direction.

Positive Rotation Negative Rotation 90° -270°

+ degree Terminal side Initial side 180° 0° - 180° 0° Initial side Terminal side - degree

- 90° 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° c. 990°

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.