1. Graphing sin(x) and cos(x)
Section 4.4
Graphing sin(x) and cos(x)

2. Periodic:
A function is periodic if for some real number α, f (x+ α) = f (x) for each x in the domain.
The least positive value for α for which f (x+ α) = f (x) is the period of the function.
English – it is periodic if it repeats itself
English – the period is the distance it takes to repeat itself

3. Examples…

4. Graph on your calc:
y = sin(x) and determine if periodic
(ZOOM – TRIG)

5. Properties of sin(x)
Period = 2
Domain: (-∞, ∞)
Range: [-1, 1]

6. Graph cos x

7. Graph cos x

8. Properties of cos(x)
Period = 2
Domain: (-∞, ∞)
Range: [-1, 1]

9. Amplitude The amplitude of the functions
y = A sin Ө and y = A cos Ө is the absolute value of A.

10. Period = y = a sin (bx +c) + d y = a cos (bx +c) + d
The distance it takes to go “one wave”

11. State the amplitude and the period and graph:

12. State the amplitude and the period and graph:

13. State the amplitude and the period and graph:

14. State the amplitude and the period and graph:

15. Homework
Worksheet