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Circular Trig

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. terminal side angle initial side

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: Draw each angle.

A complete rotation of a ray results in an angle measuring 360. We don’t have to stop there! 137 more 137 is coterminal with 497. They have the same terminal angle! We can keep adding or subtracting 360 to get more coterminal angles. 360 497 altogether!

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° - 360° - 360° = 35° b) 187 + 360 = 173

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