Graphing Sin and Cosine Vertical Transformations

vertical stretch by a factor of  $$2$$  

vertical shrink by a factor of  $$\frac{1}{2}$$  

right  $$\frac{\pi}{4}$$  

left  $$\frac{\pi}{4}$$  

up  $$2$$  

$$y=2\sin x$$  

$$y=2\cos x$$  

$$y=2\cos2\pi x$$  

$$y=2\pi\ \sin2x$$  

$$y=2\pi\sin2x$$  

y = 2

y = -2

y = -1

y = 0

vertical compression of 1/2 , horizontal stretch to a period of 4Π, vertical shift of 1 unit up, phase shift of Π units left

vertical stretch of 2, horizontal compression to a period of 4Π , vertical shift of 2 units up, phase shift of Π units left

vertical stretch of 1/2 , horizontal compression to a period of 2Π , vertical shift of 1 unit up, phase shift of Π units left

vertical compression of 1/2 , horizontal stretch to a period of 2Π , vertical shift of 1 unit down, phase shift of Π units left

3

1/3

1

-3

2π

-2π

3

$$f\left(x\right)=-2\sin\left(x-\frac{\pi}{6}\right)$$  

$$f\left(x\right)=2\sin\left(x-\frac{\pi}{6}\right)$$  

$$f\left(x\right)=-2\sin\left(x+\frac{\pi}{6}\right)$$  

$$f\left(x\right)=2\sin\left(x+\frac{\pi}{6}\right)$$  

 y = 2 cos x

y = sin x

y = 2 sin x

y = sin 2x 

period

amplitude

phase shift

vertical shift