A periodic function is one which repeats itself over and over in horizontal direction.
What is period ?
The period of a periodic function is the length of one repetition or cycle
What is amplitude ?
The amplitude is the vertical distance between a maximum point and the principal axis.
For the following sine and cosine functions find
i) amplitude
ii) period
Problem 1 :
f(x) = sin 4x
Solution :
f(x) = sin 4x
Amplitude (A) = 1, B = 4, period = 2π/4 ==> π/2
Problem 2 :
f(x) = cos 5x
Solution :
f(x) = cos 5x
Amplitude (A) = 1, B = 5, period = 2π/5
Problem 3 :
f(x) = sin x
Solution :
f(x) = sin x
Amplitude (A) = 1, B = 1, period = 2π/1 ==> π
Problem 4 :
f(x) = 4 cos x
Solution :
f(x) = 4 cos x
Amplitude (A) = 4, B = 1, period = 2π/1 ==> 2π
Problem 5 :
f(x) = -2 sin x
Solution :
f(x) = -2 sin x
Amplitude (A) = 2, B = 1, period = 2π/1 ==> 2π
Problem 6 :
f(x) = 2 sin (4x)
Solution :
f(x) = 2 sin (4x)
Amplitude (A) = 2, B = 4, period = 2π/4 ==> π/2
Problem 7 :
f(x) = 3 sin (2/3) x
Solution :
f(x) = 3 sin (2/3) x
Amplitude (A) = 3, B = 2/3, period = 2π/(2/3) ==> 3π
Problem 8 :
f(x) = -4 cos 5x
Solution :
f(x) = -4 cos 5x
Amplitude (A) = 4, B = 5, period = 2π/5
Problem 9 :
f(x) = 3 cos 2x
Solution :
f(x) = 3 cos 2x
Amplitude (A) = 3, B = 2, period = 2π/2 ==>π
Problem 10 :
f(x) = sin 2x
Solution :
f(x) = sin 2x
Amplitude (A) = 1, B = 2, period = 2π/2 ==>π
Problem 11 :
f(x) = sin (x/3)
Solution :
f(x) = sin (x/3)
Amplitude (A) = 1, B = 1/3, period = 2π/(1/3) ==> 6π
Problem 12 :
f(x) = sin 0.6x
Solution :
f(x) = sin (0.6x)
Amplitude (A) = 1, B = 0.6, period = 2π/0.6
= 2π/(6/10)
= 20π/6
= 10π/3
Problem 13 :
f(x) = sin 4x + 1
Solution :
f(x) = sin (4x) + 1
Amplitude (A) = 1, B = 4, period = 2π/4
= π/2
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM