Section 6­4 Trig B.notebook
Warm­Up:
1. What does the expression π + 2πn mean?
4
What does n represent?
November 10, 2016
Use a graphing calculator to graph the sine and cosine functions on the same set of axes for [0,2π]. Use the graphs to find the values of x, if any, for which each of the following is true.
a) sin x ≤ cos x
b) sin x = ­cos x
c) (sin x)(cos x) > 1
d) sin x+cos x=1
2. Find where sin θ = 1/2 between 0 and 2 π.
Feb 24­9:50 AM
Questions on Sec. 6.3
Nov 9­8:12 AM
6.4 Amplitude & Period of Sine & Cosine Functions
• I can identify the amplitude and period for the sine and cosine functions given the equation of trig function and write an equation given the amplitude and period.
Dec 14­8:10 PM
1. Graph y = sin θ (same as y = sin x). Leave it on your calculator.
Feb 24­10:30 AM
What is the maximum value of sin θ and cos ?
θ
2. Graph y = 3 sin θ. Compare it to #1.
3. Graph y = 2 sinθ. Compare it to #1.
4. Graph y = 1/2 sin θ. Compare it to #1.
What is the maximum value of A sin θ and A cos ?
θ
What does putting a number in front of sine do to the graph?
Dec 14­2:28 PM
Oct 20­8:19 AM
1
Section 6­4 Trig B.notebook
The absolute value of A is called the amplitude of the function. y = Asin θ and y = Acos θ November 10, 2016
Ex: What is the amplitude of y = 4 cos x? Sketch a graph.
EX: y = 2 sin θ
2
Ex. Find the amplitude of y = ­2sin θ. Sketch a
graph.
-2
Oct 20­8:25 AM
Warm­Up
Nov 9­8:18 AM
Graphing Calculator:
1) Graph y = 1/4 sin x
2) Graph y = 8 cos x
On the same screen, graph
y = sin x
y = sin 2x
y = sin 3x
y = sin .5x
y = sin .25x
Describe what happens to the graph as the number in front of x changes? Nov 9­9:15 AM
Consider y = sin kθ
The period of y = sin kθ and y = cos kθ is 2π k
where k > 0
Oct 20­8:36 AM
Feb 24­9:59 AM
Find the period of y = sin θ. Sketch a graph.
2
Try This: Find the period and amplitude of y = cos θ . Sketch a graph.
4
Oct 20­8:38 AM
2
Section 6­4 Trig B.notebook
Find the amplitude and period of y = 5cos 2θ. Sketch a graph.
November 10, 2016
Sec. 6.4 part2
A signal buoy between the coast of Hilton Head, S. Carolina, and Savannah, Georgia, bobs up and down in a minor squall. From the highest point to the lowest point, the buoy moves a distance of 3.5 feet. It moves from its highest point down to its lowest point and back to its highest point every 14 seconds. Find an equation of the motion for the buoy assuming that it is at its equilibrium point at t = 0 and the buoy is on its way down at that time. What is the height of the buoy at 8 seconds and at 17 seconds?
Write an equation of a sine function with amplitude 2 and period π
2
How do we know if it is a sine function or a cosine function?
Oct 20­8:49 AM
Oct 22­8:28 AM
Assignment: p. 374 #17­29 odd, 37­47 odd, 56
Oct 20­8:56 AM
Nov 10­8:27 AM
3