Post on 24-Feb-2016
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Unit 5 Day 9
Graphs of Trig Functions
Warm-upWarm-up: Graph the following and state the vertex and axis of symmetry:• y = 3x2
• y = x2 +5• y = 3(x-4)2 -7 2. Solve the triangle if Angle A = 60, c = 8, b = 10
3. Solve the trigonometric equation: 2tan(x)sin(x) = 2tan(x)a = 9.2, B = 71, C = 49
x = 90°
Vertex: (0,0) AOS: x = 0
Vertex: (0,5) AOS: x = 0
Vertex: (4,-7) AOS: x = 4
Homework AnswersPart 1:1. A2. B3. C4. E5. F6. D
Part 2:Xmin: 0Xmax : 360Ymin : -5Ymax : 5
Graph A:Max (45, 4)Min (135, -2)Increasing (0,45)U(135, 225)U(315, 360)Decreasing (45, 135)U(225,315)Positive (0,105) U (165,285)Negative(105,165) U (285,360)Period: 180Midline: y = 1
Homework Answer ContinuedGraph B:Max: NoneMin: NoneIncreasing (0,90)U(90, 180)U(180, 270)U(270, 360)Decreasing: NeverPositive: (45,90)U(135,180)U(225,270)U(315,360)Negative: (0,45)U(90,135)U(180, 225)U(270, 315)Period: 90Midline: y = 0
Graph C:Max: (0, 1) and (360,1)Min: (180,-3)Increasing (180,360)Decreasing: (0,180)Positive (0,45)U(315,360)Negative(45,315)Period: 360Midline: y = -1
Amplitudes, Midlines, and Period
Amplitude
What are the similarities and differences between the 3 graphs??
Given the standard equation y=asin(bx), How does “a”
affect the graph?The “a” affects the height of the graph.
Summary:Amplitude:*Amplitude is the height of the graph from the midline*a. A graph in the form of:
has an amplitude of .
b. The amplitude of a standard sine or cosine graph is 1.
amp = | a | = | max – min | 2
Summary continuedMidline:The midline is the line that “cuts the graph in half.”The midline is halfway between the max and the min.The midline can be found by using the following formula:
When there is no vertical shift, the midline is always the x-axis (y = 0).
(Ex: y = sin(x), y = 2sin(x), y = sin(3x) all have a midline of y = 0 )
Midline is y = (Max + Min) OR y = Min + Amp 2
Midline Continued
y = sin(x)
y = sin(x) + 1
Midline moved up 1
**Notice: The amplitude did not
change.
Given the standardequation y = a sin (bx),
*How does “a” affect the graph?
*How does “b” affect the graph?
The “a” affects the height of the graphA negative “a” reflects the graph over the x-axis
The “b” affects the period of the graphRemember, period = 360 |b|
Period of a Function*Period is the length of 1 cycle.* Y = sin(x) has a period of 360.
y = cos(x) has a period of 360.
y = tan(x) has a period of 180.
Let’s go back to the graphs and take a look at what this means graphically.
360| |B
2| |
PerB
( ) sin( )f x A Bx
Think of the pi as 180 degrees!!!
360| |B
360 3601
360 360
1
360 720(1/ 2)
360 720(1/ 2)
360 1802
360 1802
( ) sin( )f x A Bx 2(180)| |
PerB
Let’s Graph one together!Notes pg. 32
We’ll graph one period in the positive direction and one period in the negative direction.
4. y = 0.5 sin (x)Amplitude: ______ Midline: ______ Period: _____
Always find the period before
graphing!
Label both axes!
Practice – you try the others!
Notes pg. 33 #5, 6, 7For each problem, graph one period in the
positive direction and one period in the negative direction.
Remember to label the axes!
Homework