Section 5.3 Trigonometric Graphs

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Section 5.3Trigonometric Graphs

• Objectives
• To graph the sine and cosine curves.
• To understand amplitudes and periods of sine and
  cosine curves.

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Class Work
Find the exact value of the function. 1. 2.
3. 4. 5.
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Describe the transformation in each
graph. 6. 7. 8. 9.
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Sine Curve
Change in t Movement of Point P Sin t (y coordinate) Corresponding graph
From 0 to From (1,0) to (0,1) Increases from 0 to 1



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Ex 1. Graph the following functions.

1. y sin x
2. y -sin x

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1. y 1 sin x
2. y 2sin x

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Cosine Curve
Change in t Movement of Point P cos t (x coordinate) Corresponding graph
From 0 to From (1,0) to (0,1) Decreases from 1 to 0



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Ex 2. Graph the following functions.

1. y cos x
2. y 2 cos x

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c) y -3cos x
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Class Work

• 10. Graph y 1 sin x
• 11. Graph y -1 cos x
• 12. Graph

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Amplitude and Period of Sine and Cosine Curves
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Ex 3. Find the amplitude and period of each
function.
a) b) c)
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Shifted Sine and Cosine Curves
The sine and cosine curves have amplitude of
, period , and phase shift b.
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Find the amplitude, period, and phase shift of
the following.
a) b) c)
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Class Work
Find the amplitude period and phase shift of the
following. 13. 14.
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Ex 5 Find the amplitude, period and phase shift
of the following.
a) b) c)
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HW 3 p429 1-13odd graph 15-39 odd - find
amp, period, and phase shift.