I'm supposed to graph y= 4+2sin (pi/6 t -pi/5)

Question

i have the vertical shift d=4
amplitude 2
level line y=4
crest line y=6
trough line y=2

but i am not sure what the period is
formula for period 2pi/b
in this case 2pi/pi/6 => 12pi/pi

do the pi's cancel, leaving the period at 12????

am i doing this right?

Answer 1

You are correct,
for y = sin kx, the period is 2π/k

in your case you have 2π/(π/6)
= 2π(6/π) = 12 (units of t)

I am surprised you don't have to find the phase shift
to get the correct phase shift your equation should be in the form
y = 4 + 2sin[ (π/6)( t - 6/5) ]

so the phase shift is 6/5 units to the right.

Answer 2

I did have to find those too but i was stuck on the Period!
thank you so very much!