Consider the function fxcos01x fxcos01x aFor the argument o

Consider the function f(x)=cos(0.1x) f(x)=cos(0.1x) .

a.For the argument of cosine , 0.1x , to vary by 2?, the value of x must vary from 0 to

b. Consider the function f(x)=sin(2?x) f(x)=sin(2?x) .

For the argument of sine, 2?x , to vary by 2?, the value of x must vary from 0 to

Solution

(a)

f(x)=cos(0.1x)

(i)

to vary by 2pi

it means that

From 0:

0.1x=0

x=0

To 2pi:

0.1x=2pi

x=20pi

(ii)

If f(x)=cos(Bx)

Period = 2pi/B

for f(x)=cos(0.1x)

B=0.2

period = 2pi/0.1

period=20pi

(b)

f(x)=sin(2pi x)

(i)

From 0:

2pix =0

x=0

To 2pi:

2pix =2pi

x=1

(ii)

If f(x)=sin(Bx)

period =2pi/B

Here , we have f(x)=sin(2pi x)

B=2pi

period =2pi/2pi

time period =1.......Answer