1. Lesson 4.2

2. A circle with center at (0, 0) and radius 1 is called a unit circle. The equation of this circle would be (1,0) (0,1) (0,-1) (-1,0)

3. Let's pick a point on the circle. We'll choose a point where the x is 1/2. If the x is 1/2, what is the y value? (1,0) (0,1) (0,-1) (-1,0) x = 1/2

4. (1,0) (0,1) (0,-1) (-1,0)  Now, draw a right triangle from the origin to the point when x = ½. Use this triangle to find the values of sin, cos, and tan.

6. (1,0) (0,1) (0,-1) (-1,0)  Find the sin, cos, and tan of the angle

7. How many degrees are in each division? 45° 90° 0°0° 135° 180° 225° 270° 315°

8. How about radians? 45° 90° 0°0° 135° 180° 225° 270° 315°

9. How many degrees are in each division? 30° 90° 0°0° 120° 180° 210° 270° 330° 60° 150° 240° 300°

10. How about radians? 30° 90° 0°0° 120° 180° 210° 270° 330° 60° 150° 240° 300°

12. Let’s think about the function f(  ) = sin  Domain: All real numbers. Range: -1  sin   1 (1, 0) (0, 1) (-1, 0) (0, -1)

13. Let’s think about the function f(  ) = cos  Domain: All real numbers Range: -1  cos   1 (1, 0) (0, 1) (-1, 0) (0, -1)

14. Let’s think about the function f(  ) = tan  Domain: Range:All real numbers x ≠ n(  /2), where n is an odd integer

15. Trig functions:

16. Look at the unit circle and determine sin 420°. So sin 420° = sin 60°. Sine is periodic with a period of 360° or 2 .

17. Reciprocal functions have the same period. PERIODIC PROPERTIES sin(  + 2  ) = sin  cosec(  + 2  ) = cosec  cos(  + 2  ) = cos  sec(  + 2  ) = sec  tan(  +  ) = tan  cot(  +  ) = cot  This would have the same value as 1 Subtract the period until you reach an angle measure you know.

18. Positive vs. Negative & Even vs. Odd Remember negative angle means to go clockwise Even if: f(-x) = f(x)Odd if: f(-x) = -f(x)

19. Cosine is an even function.

20. Sine is an odd function.

21. EVEN-ODD PROPERTIES sin(-  ) = - sin  (odd) cosec(-  ) = - cosec  (odd) cos(-  ) = cos  (even) sec(-  ) = sec  (even) tan(-  ) = - tan  (odd) cot(-  ) = - cot  (odd) Problem Set 4.2