HOW TO FIND AMPLITUDE AND PERIOD OF SINE AND COSINE FUNCTIONS

For the following sine and cosine functions find 

i) amplitude 

ii) period

Problem 1 :

f(x) = sin 4x

Solution

Problem 2 :

f(x) = cos 5x

Solution

Problem 3 :

f(x) = sin x

Solution

Problem 4 :

f(x) = 4 cos x

Solution

Problem 5 :

f(x) = -2 sin x

Solution

Problem 6 :

f(x) = 2 sin (4x)

Solution

Problem 7 :

f(x) = 3 sin (2/3) x

Solution

Problem 8 :

f(x) = -4 cos 5x

Solution

Problem 9 :

f(x) = 3 cos 2x

Solution

Problem 10 :

f(x) = sin 2x

Solution

Problem 11 :

f(x) = sin (x/3)

Solution

Problem 12 :

f(x) = sin 0.6x

Solution

Problem 13 :

f(x) = sin 4x + 1

Solution

Answer Key

1)  Amplitude (A) = 1, B = 4, period = π/2

2)  Amplitude (A) = 1, B = 5, period = 2π/5

3) Amplitude (A) = 1, B = 1, period = π

4)  Amplitude (A) = 4, B = 1, period = 2π

5)  Amplitude (A) = 2, B = 1, period = 2π

6)  Amplitude (A) = 2, B = 4, period = π/2

7) Amplitude (A) = 3, B = 2/3, period = 3π

8)  Amplitude (A) = 4, B = 5, period = 2π/5

9) Amplitude (A) = 3, B = 2, period = π

10)  Amplitude (A) = 1, B = 2, period = π

11)  Amplitude (A) = 1, B = 1/3, period = 6π

12)  Amplitude (A) = 1, B = 0.6, period = 10π/3

13)  Amplitude (A) = 1, B = 4, period = π/2

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