Question

How do you sketch the graph of `f(x) = 3sin^2(2x + Pi/4)`?

Answer 1

See the graph of this sine wave and explanation.

Explanation:

`0 <= y = 3 sin^2( 2 x + pi/4 ) in 3 [0, 1 ] = [ 0, 3 ]`

`y = 3 sin^2( 2 x + pi/4 ) = 3/2 ( 1 - cos ( 2 ( 2 x + pi/4 ) ) )`

`= 3/2 - 3/2 cos ( 4 x + pi/2 ) = 3/2 + 3/2 sin 4x`.

So, this a sine wave.

The period `= (2pi)/4 = pi/2`.

The amplitude `= 3/2`.

The axis is # y = 1.5

Now see the wave, withe these aspects duly depicted.
graph{(y-3/2 - 3/2 sin (4x) )(y-3+0x)(y-1.5+0x)(x-1/2pi+0.0001y)(x+1/2pi+0.0001y) = 0[-3.4 3.4 -0.2 3.2]}