Basic Terms An angle is formed by rotating

Basic Terms • An angle is formed by rotating a ray around its endpoint. • The ray in its starting position is called the initial side of the angle. • The ray’s location after the rotation is the terminal side of the angle.

Basic Terms • Positive angle: The rotation of the terminal side of an angle counterclockwise. • Negative angle: The rotation of the terminal side is clockwise.

Example 1: Label each angle.

A complete rotation of a ray results in an angle measuring 360. We don’t have to stop there! 137 more 497 altogether! 360 Two angles drawn in standard position and have a common terminal side are called Coterminal. 137 is coterminal with 497. They have the same terminal angle! We can keep adding or subtracting 360 to get more coterminal angles.

Example 2: For the angles below, find the smallest positive coterminal angle. (Add or subtract 360 as may times as needed to obtain an angle with measure greater than 0 but less than 360. ) a) 1115 b) 187 a) 1115° - 360° = 35° b) 187 + 360 = 173

Reference Angles • For any given angle, its reference angle is an acute version of that angle. In standard position, the reference angle is the smallest angle between the terminal side and the x-axis.

What’s a radian? • You’re used to thinking of a circle in terms of degrees: 360° is the whole circle. 180° is half the circle, etc. . . • Radian measure is just a different way of talking about the circle. • Just as we can measure a football field in yards or feet--we can measure a circle in degrees or in radians!

Think about what the word radian sounds like… it sounds like “radius, ” right? It turns out that a radian has a close relationship to the radius of a circle.

Example 3: Convert each degree measure to radians. (a) 30° (b) 120° (c) 60° (d) 270° (e) 104 °

Example 3: Convert each radian measure to degrees.

Write these down in your notes! If you memorize them, it will make converting from radians to degrees (and vice versa) much easier!

Assignment • Complete the coterminal and reference angle worksheet – Turn into red basket when completed – If not completed in class it is homework