1. Unit 4: Intro to Trigonometry

2. Trigonometry The study of triangles and the relationships between their sides and angles

3. Let’s look at an angle in standard position, where the initial side is ALWAYS on the positive x-axis and the vertex is at the origin. The terminal side can be anywhere and defines the angle. A positive angle is described by starting at the initial side and rotating counterclockwise to the terminal side (angle  ). terminal side initial side vertex   A negative angle is described by rotating clockwise (angle  ).

4. Depending upon the degree measure of the angle, the terminal side can land in one of the four quadrants. Angles can be larger than 360º by simply wrapping around the quadrants again. (450º, 540º, 630º, 720º, etc.) I II III IV I II III IV     I II III    

5. Name the quadrant of the terminal side. 1)140 o 7) 80 o 2)315 o 8) -475 o 3)-168 o 9) -25 o 4)475 o 10) 1030 o 5)-340 o 11) -1030 o 6) 670 o 12) -225 o II IV III II I IV I III IV I II

6.   Angles  and  are coterminal since they share the same sides. Coterminal Angles are angles that share the same terminal side, but have different angle measures. There are also several other angles that are coterminal to .

7. To find a coterminal angle: add or subtract 360º (or any multiple of 360 o ) to the given angle . Both are coterminal angles to  Example: 35 + 360 = 395º  = 35º 35 – 360 = -325º Find a negative and positive coterminal angle to -425 o

8. Find one positive and one negative coterminal angle for each angle below. 1)140 o 7) 80 o 2)315 o 8) -475 o 3)-168 o 9) -25 o 4)475 o 10) 1030 o 5)-340 o 11) -1030 o 6) 670 o 12) -225 o