Monday, May 13, 2013

Find the period, range, and amplitude of the cosine function y= -3 cos 4x

We use the general form of the equation to determine parameters 
%0D%0Af%28x%29=a%2Acos%28omega%2Ax%2Btheta%29%2Bf%5B0%5D%0D%0A
%0D%0Af%28x%29=-3%2Acos%284%2Ax%2B0%29%2B0%0D%0A 

This comparison tells us the following 

Period:
%0D%0Aomega=%282+%2Api%29%2FT%0D%0A
so 
%0D%0AT=%282+pi%29%2Fomega=%282%2A+pi%29%2F4=pi%2F2%0D%0A 


Range: 
%0D%0Af%5B0%5D-abs%28a%29%3C=+x+%3C=f%5B0%5D%2Babs%28a%29%0D%0A 

which is
%0D%0A-3%3C=x%3C=3%0D%0A 


Amplitude:
%0D%0Aa=abs%28-3%29=3%0D%0A 





:)
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