A pre-calc function question, please help.?

So doubling the number in front of t resulted in half the period length. In general y = sin(kt) will have a period of 2? /k.

Do you see why? You can use that discovery to make a sine function with period 6 period 2? /k = 6, so k =?

/3 y = sin(?/3)t will have a period of 6. With that start it is easy to double the amplitude to y = 2sin(?/3)t which will still have a period of 6. Finally a vertical shift of 1 is obtained by just adding 1 y = 2sin(?/3)t + 1 is the desired result.

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