Finding Period and Amplitude for y = 1/2 cos(2x/3)

[andie]

I have the equation y=1/2cos(2x/3)
The period is 3? and the amplitude is 1/2
I know how to get the amplitude, but I need help on how to get the period

 

[royhaas]

Re: Finding Period and Amplitude

Show that \(\displaystyle y(x+3\pi)=y(x)\).

 

[wjm11]

Re: Finding Period and Amplitude

I have the equation y=1/2cos(2x/3)
The period is 3? and the amplitude is 1/2
I know how to get the amplitude, but I need help on how to get the period

Use the coefficient of x. In general, let’s call it variable B. The relationship between B and the period of the function, P, is simple:

B = 2pi/P

The “2pi” applies to both sine and cosine functions. This can also be rearranged to read

P = 2pi/B

In this case B = 2/3. Therefore,

P = 2pi/(2/3) = 3pi

If you are working in degrees rather than radians, use 360 in place of 2pi.

Hope that helps.