1. Pre-Calculus Honors 4.5, 4.6, 4.7: Graphing Trig Functions
HW: 4.5: p.300 (46-56 even)
4.5: p.300 (43-53 odd, skip 49)
Graphing Test: : Friday, 3/18

2. 4.5: Graph of y = sin x
Sine graph is periodic (period for y = sin x is ).
Five Key Points:
Intercepts, Max,
and Min.
Amplitude = half
the distance bet.
the max. and min.
(amplitude for
y = sin x is 1.)

3. 4.5: Graph of y = cos x
Cosine graph is periodic (period for y = cos x is ).
Five Key Points:
Intercepts, Max,
and Min.
Amplitude = half
the distance bet.
the max. and min.
(amplitude for
y = cos x is 1.)

4. Graphing: Amplitude = Period = Phase Shift : solve equations and .
This will give you the left and right endpoints of a period.
Vertical Shift =
The graph of is a reflection in the x-axis of

5. Find the period and amplitude of the graph.
1.) 2.) 3.)

6. Sketch one period of the graph.
1.)
2.)

7. Sketch one period of the graph.
3.)
4.)

8. Sketch one period of the graph.
5.)
6.)

9. Pre-Calculus Honors 4.5, 4.6, 4.7: Graphing Trig Functions
HW: 4.6: p.311 (10-14 even, 22, 28, 42, 44)
Graphing Test: : Friday, 3/18

10. 4.6: Graph of y = tan x
Tangent graph is periodic (period for y = tan x is ).
Vertical asymptotes =
X-intercepts =

11. Graphing: Asymptotes = solve equations and .
X-intercept: half way between asymptotes.
Period = distance between two consecutive asymptotes.
The graph of is a reflection
in the x-axis of

12. Sketch one period of the graph.
1.)
2.)

13. 4.6: Graph of y = cot x
Cotangent graph is periodic (period for y = cot x is ).
Vertical asymptotes =
X-intercepts =

14. Graphing: Asymptotes = solve equations and .
X-intercept: half way between asymptotes.
Period = distance between two consecutive asymptotes.
The graph of is a reflection
in the x-axis of

15. Sketch one period of the graph.
1.)
2.)

16. Pre-Calculus Honors 4.5, 4.6, 4.7: Graphing Trig Functions
HW: 4.6: p.311 (16-26 even, skip 22)
Graphing Test: : Friday, 3/18

17. 4.6: Graphing Cosecant and Secant
Cosecant: graph sine first.
Where sin x = 0, csc x has a vertical asymptote.
Secant: graph cosine first.
Where cos x = 0, sec x has a vertical asymptote.

18. Sketch one period of the graph.

19. Sketch one period of the graph.

21. 4.7: Graph of y = arcsin x
Recall: The domain was restricted for arcsin to produce a function.
This is the inverse function meaning the x and y values for the graph of y = sin x have switched.
The inverse is the graph of
x = sin y over the domain:

22. 4.7: Graph Inverse Functions

23. Review Questions
P ( odd, odd)