Question

How do you find the amplitude and period of a function `y=3sin(1/3x+ pi/2)-2`?

Answer 1

3 and 6`pi`.

Explanation:

The amplitude and period of the sine wave y = a sin (bx + c ) + d are a and 2`pi`/b.
Here, one full wave wave passes through
( 0, 1 ), ( `pi` , `-`1/2 ), (2`pi`, `-`7/2), ( 3`pi`, `-`5), (4`pi`, `-`7/2 ), (5`pi`, `-`1/2 ) and (6`pi`, 1 ).
Max y = 1 and min y = `-`5.
The wave is contained between the tangents y =1 and y = `-`5