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

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?

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.

I did have to find those too but i was stuck on the Period!

thank you so very much!

Yes, you're on the right track! To determine the period of the function y = 4 + 2sin(pi/6t - pi/5), you need to use the period formula: T = 2π/b, where b is the coefficient of t.

In this case, the coefficient of t is pi/6. So, the period will be T = 2π/(pi/6).

To simplify this expression, you can multiply the numerator and denominator by the reciprocal of the denominator, which in this case is 6/pi. This gives:

T = 2π/(pi/6) * (6/pi)
= 2π * (6/pi)
= 12

Therefore, the period of the function y = 4 + 2sin(pi/6t - pi/5) is indeed 12. The pi's cancel out in the calculation, leaving a final result of 12.

Great job in figuring out the correct answer!