# How do you write an equation of a sine function with amplitude 4, period pi, phase shift pi/2 to the right, and vertical displacement 6 units down?

##### 1 Answer

#### Answer:

#### Explanation:

The standard form of a sine function is

#y=asin[b(x-h)]+k#

where

#a# is the amplitude,#(2pi)/b# is the period,#h# is the phase shift, and#k# is the vertical displacement.

We start with classic

graph{(y-sin(x))(x^2+y^2-0.075)=0 [-15, 15, -11, 5]}

*(The circle at (0,0) is for a point of reference.)*

The amplitude of this function is

Our function is now

graph{(y-4sin(x))(x^2+y^2-0.075)=0 [-15, 15, -11, 5]}

The period of this function—the distance between repetitions—right now is

Our function is now

graph{(y-4sin(2x))(x^2+y^2-0.075)=0 [-15, 15, -11, 5]}

This function currently has no phase shift, since

Our function is now

graph{(y-4sin(2(x-pi/2)))((x-pi/2)^2+y^2-0.075)=0 [-15, 15, -11, 5]}

Finally, the function currently has no vertical displacement, since

Our function is now

graph{(y-4sin(2(x-pi/2))+6)((x-pi/2)^2+(y+6)^2-0.075)=0 [-15, 15, -11, 5]}