Lesson 4.4 Graph of sine and cosine

Draw

draw Graph of y=sinx

Multiple Choice

How the graphs of f(x)=cos⁡x and g (x)=5 cos⁡x  

Multiple Choice

How the graphs of f(x)=cos⁡x and g (x)=-3 cos⁡x  

• vertical expation with a factor 3

• Reflection over x axis

• Vertical expansion with Reflection over x-axis

• Vertical expansion with Reflection over y-axis

Multiple Choice

How the graphs of f(x)=sin⁡x and g (x)=-4 sin⁡x  

Multiple Choice

Describe how the graphs of f(x)=cos⁡x and g (x)=cos x/2 are related

• Period is $$4\pi$$  1 cycle will complete in $$4\pi$$  

• Period is $$2\pi$$  

• 1 cycle will complete in $$2\pi$$  

Multiple Choice

find the period and frequency of y=cos $$\cos\ \left(\frac{1}{3}\right)x$$  

• Period is $$6\pi$$   and frequency is $$\frac{1}{6\pi}$$  

• Period is $$3\pi$$   and frequency is $$\frac{1}{3\pi}$$  

• Period is $$\frac{1}{6}\pi$$   and frequency is $$6\pi$$  

Multiple Choice

State the amplitude, period, frequency, and phase shift of $$y=\sin\left(3x-\frac{\pi}{2}\right)$$  Then graph  two periods of the function.

• amplitude =1

  period= $$\frac{2\pi}{3}$$  

  frequency= $$\frac{3}{2\pi}$$  

  phase shift= $$\frac{\pi}{6}$$  

• amplitude =none

  period= $$\frac{3}{2\pi}$$  

  frequency= $$\frac{2\pi}{3}$$  

  phase shift=6

• amplitude =2

  period= $$\frac{3}{2\pi}$$  

  frequency= $$\frac{2\pi}{3}$$  

  phase shift=0

• amplitude =0

  period= $$\frac{3}{2\pi}$$  

  frequency= $$\frac{2\pi}{3}$$  

  phase shift=6

Multiple Choice

State the amplitude, period, frequency, and phase shift of $$y=5\sin\left(3x-\frac{\pi}{2}\right)\ +2$$  Then graph  two periods of the function.

• amplitude =5

  period= $$\frac{2\pi}{3}$$  

  frequency= $$\frac{3}{2\pi}$$  

  phase shift= $$\frac{\pi}{6}$$  

  vertical shift =2

• amplitude =1

  period= $$\frac{3}{2\pi}$$  

  frequency= $$\frac{2\pi}{3}$$  

  phase shift=6

  vertical shift =3

• amplitude =5

  period= $$\frac{3}{2\pi}$$  

  frequency= $$\frac{2\pi}{3}$$  

  phase shift=0

  vertical shift =3

• amplitude =5

  period= $$\frac{3}{2\pi}$$  

  frequency= $$\frac{2\pi}{3}$$  

  phase shift=6

  vertical shift =2