1. 4.2 Day 1 Trigonometric Functions on the Unit Circle Pg. 472 # 6-10 evens, 16-24 evens, 46, 54, 56, 60 For each question (except the 0 o, 90 o, 180 o, and 270 o positions): Draw the triangle at the correct position on the unit circle. Label the side lengths. Then, find the answer. Do NOT throw away this packet. Keep it until you can do all of these questions quickly and automatically.

2. Label the corresponding angles in degrees for each position in radian:

3. What is the unit circle? A circle with radius = 1 unit Why are we interested in this circle? It provides convenient (x,y) values as we work our way around the circle. Any (x,y) point on the circle would be at the end of the hypotenuse of a right triangle that extends from the origin, such that

4. Trigonometric Values at 0 o, 90 o, 180 o, and 270 o In Radians: ___________________ t = arc length on the unit circle in degrees or radians. For any point (x,y) found on the unit circle, sin t = y cos t = x tan t = y/x

5. Trigonometric Values at 45 o, 135 o, 225 o, and 315 o All 45 o - 45 o - 90 o triangles on a unit 1. 45 o (Radians: ) circle have these side lengths: Draw the triangle. Label the side lengths. Find sin, cos, and tan.

6. 2. 135 o (Radians: ) Draw the triangle. Label the side lengths. Find sin, cos, and tan.

7. 3. 225 o (Radians: ) Draw the triangle. Label the side lengths. Find sin, cos, and tan.

8. 4. 315 o (Radians: ) Draw the triangle. Label the side lengths. Find sin, cos, and tan.

9. Trigonometric Values at 30 o, 150 o, 210 o, and 330 o 5. 30 o (Radians: ) Draw the triangle. Label the side lengths. Find sin, cos, and tan. All 30 o - 60 o - 90 o triangles on a unit circle have these side lengths:

10. 6. 150 o (Radians: ) Draw the triangle. Label the side lengths. Find sin, cos, and tan.

11. 7. 210 o (Radians: ) Draw the triangle. Label the side lengths. Find sin, cos, and tan.

12. 8. 330 o (Radians: ) Draw the triangle. Label the side lengths. Find sin, cos, and tan.

13. Trigonometric Values at 60 o, 120 o, 240 o, and 300 o All 30 o - 60 o - 90 o triangles on a unit circle have these side lengths: 9. 60 o (Radians: ) Draw the triangle. Label the side lengths. Find sin, cos, and tan.

14. 10. 120 o (Radians: ) Draw the triangle. Label the side lengths. Find sin, cos, and tan.

15. 11. 240 o (Radians: ) Draw the triangle. Label the side lengths. Find sin, cos, and tan.

16. 12. 300 o (Radians: ) Draw the triangle. Label the side lengths. Find sin, cos, and tan.