Graphs of Sine and Cosine Functions You

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Graphs of Sine and Cosine Functions Youll need
graph paper

• 4.5

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Unit Circle Activity

• On Graph paper use a radius of 7in to represent
  the radius of your unit circle.
• Then give both the fractional and decimal value
  of your trig function for each value of theta on
  the unit circle. (Do not include the last value
  of theta for your quadrant) i.e. 90, 180, 270, 360

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12 Groups
Only need one graph per group

• Groups 1-4 Sine
• Groups 5-8 Cosine
• Groups 9-12 Tangent
• Group 4n1 Q1
• Group 4n2 Q2
• Group 4n3 Q3
• Group 4n4 Q4

n is a whole
Ex Group 7 7 4(1)3 Cosine Q3
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• Label with as increases, trigfunction( )
  increases/decreases.
• Ex for sine of Q1
• as increases, increases.

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Graph the sine and cosine functions
Everyone needs to do their own!
Everyone is starting with sine

• Graph the sine function on a new piece of graph
  paper
• Label your x-axis in radians in multiples
• of . Use 1 square for each measure
• On your y-axis label . Count
  
• 1 square as ¼.
• Then graph the cosine function a separate axis.
  (use the same labels)

13 squares on each side of y-axis
8 squares on each side of x-axis
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Graph the csc and sec functions

• Graph csc with the sin graph and sec with the cos
  graph
• Then make a new graph for tan and cot
• Label your x-axis in radians in multiples of

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Ordered Pairs
x sin(x) cos(x)
-3.1416 0.0000 -1.0000
-2.6180 -0.5000 -0.8660
-2.0944 -0.8660 -0.5000
-1.5708 -1.0000 0.0000
-1.0472 -0.8660 0.5000
-0.5236 -0.5000 0.8660
0.0000 0.0000 1.0000
0.5236 0.5000 0.8660
1.0472 0.8660 0.5000
1.5708 1.0000 0.0000
2.0944 0.8660 -0.5000
2.6180 0.5000 -0.8660
3.1416 0.0000 -1.0000
3.6652 -0.5000 -0.8660
4.1888 -0.8660 -0.5000
4.7124 -1.0000 0.0000
5.2360 -0.8660 0.5000
5.7596 -0.5000 0.8660
6.2832 0.0000 1.0000

• Consider the values for x and y in the table to
  the right
• Note
• Period 2p
• Maximum y values
• Minimum y values

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Graphing the Ordered Pairs
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Graphing on Calculator

• Go to ?Y screen
• Enter function
• Choose F2, zoom 7-Trig
• Graph is plotted
• Tic marks are inunits of p/2

Try Web Graphing Utility
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Amplitude

• Defined as the absolute value of maximum or
  minimum of the function
• Try graphingy 2 sinx
• What is the amplitude
• For y a cos x or y a sin x
• The amplitude is a
• Do we need to worry about the amplitude for the
  other trig functinos?

ysinx
2
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Period of a Trig Function(Recall slide from
previous lesson)

• The functions repeat themselves
• The period is the smallest value, p for which
  f(x) f(x p)
• For sin, cos, sec, csc
• The period is 2p
• For tan and cot
• The period is p

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Period of a Trig Function

• What happens for ?
• Try graphing y sin 2x
• What is the period?
• What about
• y sin 3x
• Try y cos 0.5x
• What is the period?
• For
• Period

Same for cos, sec, csc
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Period of a Trig Function

• For tangent
• Note amplitudeis without bound
• Period is p
• For
• Period

• Predict the period fory tan (1/3 x)
• Graph it and verify your prediction

Same for cot
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Review of Transformations
Or reflection over y-axis!
Or reflection over x-axis!
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Review of Transformations
Sketch the graph Do non-rigid transformation 1st
(strech/compress) Then rigid transformations
(up/down and left/right)
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Lets investigate with graphs of trig functions!
Desmos.com
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Practice time

• Graph
• a.
• b.

Sketch each transformation of the graph
Sketch between 0 and 2pi while doing
transformations
Does the make a difference?
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H Dub

• 4-5 Pg 328 1-25odd, 35-51EOO

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Graph the sine and cosine functions

• Regraph the sine and cosine functions on two
  separate axis
• Label your graph in radians
• On your y-axis label
• Leave room above and below!
• On your x-axis label multiples of