Question

How do you write the equation of the sine function with an amplitude of 4, a period of pi/2 and a phase shift of - pi/4?

Answer 1

`y=4sin(4x+pi)`

Explanation:

The standard form of the `color(blue)"sine wave function"` is

`color(red)(|bar(ul(color(white)(a/a)color(black)(y=asin(bx+c)+d)color(white)(a/a)|)))`

where amplitude = |a| , period `=(2pi)/b`

c is the phase shift and d , the vertical shift

here a = 4 , b`=(2pi)/(pi/2)=4`

phase shift `=-c/brArrc=pi`

Substitute these values into standard form

`rArry=4sin(4x+pi)" is the equation"`