Question

How do you graph two complete cycles of `y=4cos(1/2t)`?

Answer 1

See the illustrative graph.

Explanation:

`y = 4 cos ( 1/2 t ) in 4 [ -1, 1 ] = [ - 4, 4 ]`.

The amplitude = 4.

A complete cycle = period `= (2 pi )/(1/2) = 4 pi`.

Graph for two cycles, `t in [ - 4 pi, 4 pi ]`; depicting the above

aspects
graph{(y - 4 sin ( x/2 ))(x^2-(4pi)^2)(y^2-16) = 0[-16 16 -8 8]}