Question

Is the function even or odd?
y= 1/2cos2x*sin(3Pi/2 - 2x)+3

Answer 1

what is your answer?

Answer 2

before testing f(-x), simplify the function a bit :

y= 1/2cos2x*sin(3Pi/2 - 2x)+3
y= 1/2cos2x*sin(pi + pi/2 -2x) + 3
y= 1/2cos2x*-sin(pi/2 -2x) + 3
y= 1/2cos2x*-cos(2x) + 3
y= -1/2cos^2(2x) + 3

now test to see if f(x) = f(-x)

Answer 3

IF f(-x)=f(x),function is even
and if f(-x)=-f(x) ,the function is termed as odd function

Answer 4

are we getting f(x) = -f(x) ?

our simplified y=f(x) is this :
y = f(x) = -1/2cos^2(2x) + 3

lets find f(-x) and see wat u get

Answer 5

f(x) = -1/2cos^2(2x) + 3 ---------(1)

f(-x) = -1/2cos^2(-2x) + 3
= -1/2cos^2(2x) + 3 -------(2)

Answer 6

(1) = (2), so... ?

Answer 7

The function is even

Answer 8

Thanks a lot!

Answer 9

wonderful !

Answer 10

yw