Question

Sketch one cycle of the sine curve. Y=2 sin 2 theta

Answer 1

@Hero @e.mccormick

Answer 2

@mathmale @matt101 @ganeshie8

Answer 3

I am confused on how to approach this

Answer 4

For y=sinθ, you can plot the following point on a graph to create one cycle of the basic sine curve:

(0,0)
(π/2,1)
(π,0)
(3π/2,-1)
(2π,0)

However, the equation you have above involves a couple transformations. We just need to apply these transformations to the 5 points I listed to get one cycle of the new sine curve.

For y=2sin2θ, every x-value will be halved, while every y-value will be doubled. The points you end up with are:

(0,0)
(π/4,2)
(π/2,0)
(3π/4,-2)
(π,0)

Plot those points and you have your graph!

Answer 5

Thank you so much @matt10 ! makes sense