FINDING PERIOD AND AMPLITUDE OF SINE AND COSINE FROM GRAPH WORKSHEET

Give the amplitude and period of each function graphed below. Then write an equation of each graph.

i) Amplitude

ii) Period

iii) Equation

Problem 1 :

amp-period-of-sin-cos-functionq1.png

Solution

Problem 2 :

amp-period-of-sin-cos-functionq2.png

Solution

Problem 3 :

amp-period-of-sin-cos-functionq3.png

Solution

Problem 4 :

amp-period-of-sin-cos-functionq4

Solution

Problem 5 :

amp-period-of-sin-cos-functionq5.png

Solution

Problem 6 :

amp-period-of-sin-cos-functionq6.png

Solution

Problem 7 :

amp-period-of-sin-cos-functionq7.png

Solution

Answer key

1)

i)  Amplitude

ii)  Horizontal length of one cycle or period = π

B = 2

iii) So, the equation represented by the graph is 

y = 3 sin 2x

2)

i) Amplitude = 4

ii)  Horizontal length of one cycle = 2π

B = 1

iii) So, the equation represented by the graph is 

y = 4 cos x

3)  

i) Amplitude = 2

ii)  Horizontal length of one cycle or period = 4π

B = 1/2

iii) So, the equation represented by the graph is 

y = 2 sin (1/2)x

4)

i) Amplitude = 5

ii)  Horizontal length of one cycle = 2π

B = 1

iii) So, the equation represented by the graph is 

y = -5 cos x

5)  

i)  amplitude = 3

ii)  Horizontal length of one cycle = 4π

B = 1/2

iii) So, the equation represented by the graph is 

y = 3 cos (1/2) x

6)

 i) Amplitude = 3

ii)  Horizontal length of one cycle = 4π

B = 1/2

iii) So, the equation represented by the graph is 

y = 3 sin (1/2) x

7)

i) Amplitude = 2

ii)  Horizontal length of one cycle or period = π

B = 2

iii) the equation represented by the graph is 

y = -2 sin 2 x

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