1. Trigonometric Functions Review
The test is tomorrow! You will do awesomely! Yay!

2. Example 1: Roller Coaster Height

3. Finding info from the equation
5 min lesson, 5 min exit slip!

4. Amplitude
The number in front of sin or cos is the amplitude. If there is no coefficient, it is 1.
Ignore negative/positive sign. Amplitude is distance, so it is always positive.
Amplitude for this equation = 3

5. Period
The number in front of the x (inside the parentheses) is our clue to the period. If there is no coefficient, the clue number is 1.
To find the period, divide: 360/clue
In this case, we get: 360/2 = 180º

6. Principal Axis
The number added or subtracted is the principal axis – the vertical shift.
We write the principal axis as an equation:
Here, the answer is: Y = 2

7. Review All Together Amplitude = 3 Period = 360/2 = 180º
Clue
Principal
Axis
Amplitude = 3
Period = /2 = 180º
Principal Axis: y = 2

8. Exit Slip!!! 3 minutes! Write down the: Amplitude Period
Principal Axis
Answers:
Amplitude = 4, Period = 360/3 = 120º, Principal Axis: y = -2

9. Graphing Sine and Cosine Equations
10 min lesson, 8 min exit slip!

10. Determine the View Window (calc.)
You should always be able to answer these 6:
Xmin: 0º (start) Ymin: 2 – 3 = -1
Xmax: 360º (finish) Ymax: = 5
Xscl: 90º (always) Yscl: 1

11. Graph it on your calculator (degrees)

12. Graph it on paper! You should do the following:
Draw your principal axis
Sketch the min and max lines
Sine starts in the middle, Cos starts at the maximum

13. Determine the View Window (calc.)
Amplitude = 2, Period = 360º, Pr. Axis: y = -3
You should always be able to answer these 6:
Xmin: 0º (start) Ymin: -3 – 2 = -5
Xmax: 720º (finish) Ymax: = -1
Xscl: 90º (always) Yscl: 1

14. Graph it on your calculator (degrees)

15. Exit Slip!!! 3 minutes!
Sketch the graph of the one above for: 0º ≤ x ≤ 360º !!
Answer Graph:

16. Solve Trig. Equations
5 min lesson, 4 min exit slip!

17. Determine the View Window (calc.)
Xmin = 0, xmax = 360, xscl = 90
Ymin = -5, ymax = -1, yscl = 1
Y1 = -2cos(x) – 3
Y2 = -2
2nd-Trace-Intersect

18. Determine the View Window (calc.)
Answers: 120º, 240º

19. Solve for x (should have multiple answers) for 0º ≤ x ≤ 360º!
Exit Slip!!! 3 minutes!
6 Answers: 9.65º, 110º, 130º, 230º, 250º, 350º
Explanation:
I have to give 3 significant figures for each.
Another way: 9.65 and 110º happen in the first cycle.
Because the period is 120º, add 120º to each to get 130º and 230º.
Then add 120º again to each to get 250º and 350º.

20. Real-Life Trig Problems
5 min lesson, 4 min exit slip!

21. Temperature: Find amplitude, period, pr. Axis and write eq.
Period = 12 months
Pr. Axis: average y: (16 + 7)/2 = 11.5

22. Depth: Find amplitude, period, pr. Axis and write eq.
1.5 30
4.5
Period = 360/b
12 = 360/b
B = 30
(check: 12*30 = 360)
Vertical translation = principal axis, the middle (average of max and min)
= (6 + 3)/2 = 4.5
Amplitude = ½ the distance between max & min
A = (6 – 3)/2 = 1.5