+32 Is the function y= 7 sin (2x - 3pi/2) even or odd?? How do you figure it out?
+118687 Is the function y= 7 sin (2x - 3pi/2) even or odd?? How do you figure it out?
Hi Lisa, :)
Before I give a specific answer I think it would be a good idea for you to watch this and then you will probably be able to answer your own question.
It is a bit long I know but if you odd and even really mean it should stick in your brain a whole lot better.
Basically even functions are symmetrical about the y axis so f(x)=f(-x) like y=x^2 is even
so if you reflect the graph across the y axis it will be the same.
and odd functions have 180 degree rotational symmetry about the point (0,0)
so so if you reflect the graph across the y axis AND then reflect it acraoo the x axis it will be the same. Like y=x^3 is odd
ODD f(-x)=-f(x)
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+118687 Is the function y= 7 sin (2x - 3pi/2) even or odd?? How do you figure it out?
f(x)=7 sin (2x - 3pi/2)
f(x)=7 [sin (2x) cos(3pi/2)- cos (2x) sin(3pi/2) ]
f(x)=7 [sin (2x) *0- cos (2x) *-1 ]
f(x)=7 [0+ cos (2x) ]
f(x)=7 cos (2x)
f(-x)=7cos(-2x)
f(-x)=7cos(2x)
f(-x)=f(x)
Therefore this is an even function.
