How do you find the period and amplitude of y=1/4sin(2pix)y=14sin(2πx)?

1 Answer
Jul 15, 2018

The period is T=1T=1. The amplitude is =1/4=14

Explanation:

The period TT of a periodic function f(x)f(x) is defined by

f(x)=f(x+T)f(x)=f(x+T)

Here,

f(x)=1/4sin(2pix)f(x)=14sin(2πx)............................(1)(1)

Therefore,

f(x+T)=1/4sin2pi(x+T)f(x+T)=14sin2π(x+T)

=1/2sin(2pix+2piT)=12sin(2πx+2πT)

=1/4sin(2pix)cos(2piT)+1/4cos(2pix)sin(2piT)=14sin(2πx)cos(2πT)+14cos(2πx)sin(2πT)...........................(2)(2)

Comparing equations (1)(1) and (2)(2)

{(cos2piT=1),(sin2piT=0):}

=>, 2piT=2pi

The period is T=1

For the sine function

-1<=sinx<=1

-1/4<=1/4sinx<=1/4

-1/4<=1/4sin2pix<=1/4

The amplitude is =1/4

graph{1/4sin(2pix) [-0.587, 2.113, -0.696, 0.654]}