# Period of cosine curve

• Aug 13th 2009, 05:13 PM
Mike9182
Period of cosine curve
http://my.thinkwell.com/questionbank...img/215644.gif

http://my.thinkwell.com/questionbank.../img/30657.gif

http://my.thinkwell.com/questionbank...img/215643.gif

How do you come up with the first step of the correct answer? I understnd the simplification from there.
• Aug 13th 2009, 05:20 PM
pickslides
easier way: for $\displaystyle \cos(nx)$ the period is $\displaystyle \frac{2\pi}{n}$

therefore for $\displaystyle \cos\left(\frac{\pi}{4}x\right)$ the period is $\displaystyle \frac{2\pi}{\frac{\pi}{4}} = 8$
• Aug 13th 2009, 05:26 PM
Mike9182
thanks, although how do you get the first step of the correct answer explanation I posted?
• Aug 13th 2009, 05:31 PM
pankaj
Quote:

Originally Posted by Mike9182
http://my.thinkwell.com/questionbank...img/215644.gif

http://my.thinkwell.com/questionbank.../img/30657.gif

In the first step you are using the fact that $\displaystyle f(x)=\cos x$ is periodic with period $\displaystyle 2\pi$
In general if fundamental period of $\displaystyle f(x)$ is $\displaystyle T$,then fundamental period of of $\displaystyle f(ax+b)$ is $\displaystyle \frac{T}{|a|}$, where,$\displaystyle a\neq 0$
The fundamental period of $\displaystyle f(x)=\cos x$ is $\displaystyle 2\pi$.
Therefore,the fundamental period of $\displaystyle f\left(\frac{\pi}{4}x\right)$ is $\displaystyle \frac{2\pi}{\frac{\pi}{4}}=8$