Even v. Odd Functions
I got to number 64 in section 6.3 and was having trouble figuring out which functions were even versus odd. Can anyone post a quick refresher? Thanks
posted by Carrie Desmond at 1:18 PM
Friday, January 26, 2007
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even functions are symmetric in respect to the y-axis (substituting -x results in the same equation) and odd functions are symmetric about the origin (substituting -x and -y result in the same equation)
i had trouble with d and e for this problem. do you guys understand what happens when you add the angle you are taking the tangent of, or multiply the tangent by the angle? [t*tan(t)] and [t+tan(t)]
for part d, f(t)=t*sin(t), substitute in -t, f(-t)=(-t)*sin(-t), since sin(-t)=-sin(t), f(-t)=(-t)*(-sin(t))=t*sin(t)=f(t). therefor, f(t) is an even function.
for part e, g(t)=t+tan(t), substitute in -t and -y. -g(-t)=(-t)+tan(-t), since tan(-t)=-tan(t), -g(-t)=-((-t)-tan(t))=t+tan(t)=g(t). therefor, g(t) is an odd function.
it's kind of stupid but one way i remember even vs. odd is odd and origin both start with "o" so odd functions are over the origin.
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