Question

How do you find the amplitude and period of `y=6sin(1/8x)`?

Answer 1

amplitude = 6, period `=16pi`

Explanation:

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

phase shift `=-c/b" and vertical shift" =d`

here a = 6 , `b=1/8` , c = 0 and d = 0

`rArr"amplitude" =|6|=6" and period"=(2pi)/(1/8)=16pi`