Question

write a sine function with amplitude of 3 and a period of 4pi
My guess is y=3sin(4x) @IMStuck could I get some guidance

Answer 1

I order to find the correct period, you need to remember the equivalent\[\frac{ 2\pi }{ x }\]where x is the period function. Here they are telling you what the period is, you have to find out what the number is inside the parenthesis that makes the period 4pi. If you do (4x), you are filling 4x in for the x in our equation to get\[\frac{ 2\pi }{ 4 }\]wich divides out to give you a period of 1/2 pi. that's not what you want. You actually need to divide by 1/2. Here.\[\frac{ 2\pi }{ \frac{ 1 }{ 2 } }\]because when you divide rational expressions you would flip the bottom fraction and multiply.\[2\pi \times2=4\pi \]See how that works? The equation would be y = 3sin(1/2x). You could test it out. \[\frac{ 2\pi }{ \frac{ 1 }{ 2 }}=\frac{ 2\pi }{ 1 }\times \frac{ 2 }{ 1 }=4\pi \]

Answer 2

okidoki that totally makes sense thanks a whole big lot