Trig Packet Notes #2 -...
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Trig Packet Notes #2 Graphing.notebook 1 February 28, 2017 Apr 293:37 PM Graphing Trig Functions Name: ______________________ (1,0) (0,1) (1,0) (0,1) π /2 π 3π/2 2π 1 1 π /2 π 3π/2 2π 1 1 y = sinx y = cosx x sinx 0 π/2 π 3π/2 2π Objectives: Students will be able to graph sine, cosine and tangent functions and translations of these functions. x cosx 0 π/2 π 3π/2 2π Apr 293:49 PM Properties of y = sinx and cosx -The domain of each function is ______________. -The range of each function is ___________. -The ____________ of each function is half the difference of the maximum and minimum. -Each function is ___________, which means its graph has a repeating pattern. The shortest repeating portion of the graph is called the ___________. The horizontal length of each cycle is called the __________. -The period of each function is ______.
Transcript of Trig Packet Notes #2 -...
Trig Packet Notes #2 Graphing.notebook
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February 28, 2017
Apr 293:37 PM
Graphing Trig Functions Name: ______________________
(1,0)
(0,1)
(1,0)
(0,1)
π/2 π 3π/2 2π
1
1
π/2 π 3π/2 2π
1
1
y = sinx
y = cosx
x sinx0 π/2π3π/22π
Objectives: Students will be able to graph sine, cosine and tangent functions and translations of these functions.
x cosx0 π/2π3π/22π
Apr 293:49 PM
Properties of y = sinx and cosx
-The domain of each function is ______________.
-The range of each function is ___________.
-The ____________ of each function is half the difference of the maximum and minimum.
-Each function is ___________, which means its graph has a repeating pattern. The shortest repeating portion of the graph is called the ___________. The horizontal length of each cycle is called the __________.
-The period of each function is ______.
Trig Packet Notes #2 Graphing.notebook
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February 28, 2017
Apr 293:59 PM
Examples: Determine the amplitude and period of each function graphed below.
1.) 5
-5
π/4 3π/4π/2 π 5π/4 3π/2
2.) π
-π
4π2π
Apr 293:53 PM
Amplitude and Period: The amplitude and period of the graphs y = asinbx and y = acosbx are as follows:
Amplitude = a Period = 2π
Examples: Graph the following.1.) y = 4sinx 2.) y = cos4x
b
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Apr 294:10 PM
Examples: Graph the following.1.) y = 2sin¼x 2.) y = 2cosπx
Apr 293:37 PM
x -cosx0 π/2π3π/22π
π/2 π 3π/2 2π
1
1
π/2 π 3π/2 2π
1
1
y = -sinx
y = -cosx
x -sinx0 π/2π3π/22π
Translations/Reflections of Trig Functions
(1,0)
(0,1)
(1,0)
(0,1)
Trig Packet Notes #2 Graphing.notebook
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February 28, 2017
Apr 295:27 PM
Along with reflections, graphs of trig functions can also translate left/right and up/down.
Translations of Sine and Cosine GraphsTo graph y = asin b(x - h) + k or y = acos b(x - h) + k, follow these steps:1.) Identify the amplitude a , the period 2π/b, the horizontal shift h,the vertical shift k and note any reflection.2.) Draw the horizontal line y = k, which is called the midline.3.) Find the five key points by translating the key points of y = asinbx and y = acosbx in the following order: -horizontally h units -reflect (if necessary)4.) Draw the graph through the five translated key points.
Apr 295:42 PM
Examples:
1.) Graph y = sin4x + 3
2.) y = 4cos(x - π)
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Apr 295:44 PM
3.) y = sin2(x + π/2) - 3
4.) y = -2sin[(1/2)(x - π)]
Apr 295:50 PM
Examples:
1.) Write a cosine equation that represents the graph.
ππ/2-π/4
2.) Write a sine equation that represents the graph.
4π-4π
2
1
1
-1
Trig Packet Notes #2 Graphing.notebook
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February 28, 2017
Mar 112:16 PM
Graphing Reciprocal Trig Functions
y = cscx
y = secx
Mar 112:20 PM
Examples
Graph.
1.) y = 2csc(x - π)
2.) y = -sec[2(x - π/2)] + 1
Trig Packet Notes #2 Graphing.notebook
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February 28, 2017
Apr 294:16 PM
Let's graph y = tanx by filling out the table below.
x tanx0 π/4π/23π/4π5π/43π/27π/42π
(1,0)
(0,1)
(1,0)
(0,1)
π/2 π 3π/2 2π
1
1
Apr 294:19 PM
Period and Vertical Asymptotes: The period and vertical asymptotes of the graph of y = atanbx are as follows:
- The period is π. b
- The vertical asymptotes are at odd multiples of π 2b
1.) y = 2tan3x 2.) y = 4tan2πx
Examples Graph one period of the functions below.
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Mar 112:16 PM
y = cotx
Examples Graph.
1.) y = 2cotx + 1
Mar 112:48 PM
2.) y = cot(x - π/4) + 1
3.) y = -tan[2(x + π/8)] - 1
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February 28, 2017
Apr 296:21 PM
Graph Trig Functions Homework Name: ________________
Graph the following trig functions. Label!1.) y = 2sinx 2.) y = -cos2x
3.) Fill in the blank. The graphs of the functions y = sinx and y = cosx both have a ________ of 2π. They both have an ____________ of 1.
Apr 296:23 PM
4.) Write both a sine and cosine equation of the graph below.
5.) Graph y = -4sinx. Label!
π 2π
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February 28, 2017
Apr 296:28 PM
Fill in the blanks.8.) The graph of y = cos2(x - 3) is the graph of y = cos2x translated ____ units to the right.
The graph of y = cos2x + 1 is the graph of y = cos2x translated ____ units up.
6.) Graph one period of y = 4tanπx. Label!
7.) Graph one period of y = 3tan2x. Label!
Apr 296:33 PM
9.) Graph y = 3cos(x + 3π/2) - 1. Label!
10.) Write a sine equation for the graph below.
4π 8π
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February 28, 2017
Mar 112:20 PM
Graph.
11.) y = -4cos(x + π) - 1
12.) y = 2sin[2(x - π/2)] + 1
Mar 112:20 PM
Graph.
13.) y = 3sec(x + π)
14.) y = csc[4(x - π/2)] + 1
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February 28, 2017
Mar 112:20 PM
Graph.
15.) y = cotx - 1
16.) y = 2tan[π(x + 1/2)]
Mar 11:02 PM
17.) Write a sine function with a period of π, an amplitude of 3 and a vertical shift up 2.
18.) Write a cosine function with a period of π/2, a reflection over the x-axis, an amplitude of 4 and a vertical shift down 2.
19.) Each branch of y = secx and y = cscx is a curve. Explain why these curves cannot be parabolas. Hint: Do parabolas have asymptotes?
