Question

Write the equation of a sine function that has the given characteristics. Please show the process for me if possible.
Amplitude: 4
Period: 3pi

Answer 1

The general sine function is this

\[\Large y = A\sin(Bx - C) + D\]

|A| = amplitude
T = 2pi/B is the period
C/B is the phase shift
D = used to find the midline

In this case,

amplitude = 4 so A = 4
period = 3pi so T = 3pi. Use this to find the value of B
C = 0 and D = 0

Answer 2

@jim_thompson5910 What is T?

Answer 3

And I;m mostly stuck on finding B when forming the equation out of the given info

Answer 4

T is the period
T is used instead of P. I'm not 100% sure why but I'm assuming T refers to time or something

Answer 5

ah okay

Answer 6

T = 3pi

T = 2pi/B
3pi = 2pi/B
3 = 2/B
B = ???

Answer 7

Ohhhhh okay its 2/3

Answer 8

yep so the trig equation would be...

\[\Large y = A\sin(Bx - C) + D\]

\[\Large y = 4\sin\left(\frac{2}{3}x - 0\right) + 0\]

\[\Large y = 4\sin\left(\frac{2}{3}x\right)\]

Answer 9

Sweet thanks so much

Answer 10

no problem