2. 5.3 Part 1 Trig Graphs

3. A function is periodic if its values repeat in a cycle. Sin and Cos functions repeat their values in a regular fashion. Since C = 2pi, then P(x, y) is the same as the point determined by t + 2pi Their values are unchanged by the addition of any integer multiple of 2pi. It’s period is the smallest positive number p such that f(x + p) = f(x)

4. sin and cos have period 2pi (the distance between any 2 sets of repeating points is 2 pi)

5. Graph of sin t

6. Graph cos t

8. Transformations Vertical Shifts:  f(X) + c up ‘c’ units  f(x) – c down ‘c’ units EX Graph f(x) = 2 + sin x

9. Reflections y = -f(x) – Reflects over the x-axis EX graph g(x) = -cos x

10. Ex Graph: y = 3 - cosx XY

11. Sin and Cos curves: y = a sin kx and y = a cos kx Amplitude = It is the largest value that these functions attain. Period =

12. Vertical Stretch & Shrink y = cf(x) – If c > 1, STRETCH vertically by a factor of ‘c’ – If 0 < c < 1, SHRINK vertically by a factor of ‘c’ EX Graph y = 2sin x

13. Stretch and Shrinking of sin graph

14. EX Graph: y = -3cosx

15. EX Find period and amplitude y = sin 2xy = sin ½ x y = 2cos3xy = -5sin1/3 x

16. 5-Point Graphing XY

17. Ex Graph: y = sin2x XY

18. Ex Graph: y = ½ cos2x XY

19. Remember Sin x --- 0, max, 0, min, 0 Cos x --- max, 0, min, 0, max

20. pg 429 #1-25 odd