1. Warm Up Let y = sin(3x + 1) + 2cos(3x – 1)
What is the period of the graph?
What is the amplitude of the graph?
Rewrite y in the form asin(b(x + c)).
2) Let f(x) = cos(4x) – 2sin( )
a) What is the period of the graph?
b) What is the range of the graph?
3) Write the equation of the tangent line to the curve g(x) = 1 – 2csc(5x) at the point where x = π/6

2. Trig graphs, etc.
Test Review

3. Given: Determine the amplitude of f(x). Determine the period of f(x).
Determine the horizontal shift of f(x).
Sketch one full period of the graph of f(x).

4. Given: g(x) = 4cot(2x - /6)
Determine the period of f(x).
Determine the horizontal shift of f(x).
Sketch two full periods of g(x).

5.  2 3 4 -
-2
Determine the amplitude of f(x).
Determine the period of f(x).
Determine the vertical shift of f(x)
Write a function for f(x)

6. Determine the amplitude of f(x). Determine the period of f(x).
/4
/2
3/4
-/4 
5/4
Determine the amplitude of f(x).
Determine the period of f(x).
Determine the vertical shift of f(x)
Write a function for f(x)

7. Determine the amplitude of f(x). Determine the period of f(x).
-/4
-/2
/4
/2 
3/4
Determine the amplitude of f(x).
Determine the period of f(x).
Determine the vertical shift of f(x)
Write a function for f(x)

8. Which of the following is a vertical asymptote for…
1) Y = 2csc(4x) - 1
x = /4 B. x = 3/8
C. x = D. x = /6
2) Y = 3tan (x - /3)
x= 11/6 B. x = 8/3
C. x = /4 D. x = /2

9. The average monthly consumption of firewood in Charlotte is given by the function:
where x = 0 is January 1, x = 1 is February 1,etc
During what month is consumption at a minimum? (Give the exact number and the month)
How much wood is consumed on November 1 on average ?

10. Graph 2 full periods of
y = 1 – csc(x - /6)

11. A satellite is launched from Cape Canaveral into an orbit which goes alternately north and south of the equator. Its distance from the equator over time can be approximated by a sine(cosine) wave. Suppose that the satellite is y kilometers north of the equator at time x minutes. It reaches 4500 km, its farthest point north of the equator, 15 minutes after the launch. Half an orbit later it is 4500 km south of the equator, its farthest point south. Each orbit takes 2 hours Sketch a graph with x in minutes and y in kilometers Write an equation which models the distance of the satellite from the equator How far away from the equator is the satellite 1 hour after launch?