Question

Write an equation of the sine function with amplitude 3, period 3pi/2, and phase shift pi/4.

Answer 1

So far I have
y = sin (4/3x-c)
Is this right and what do I do next?

Answer 2

@jim_thompson5910 @kropot72 hey think one of you can help me?

Answer 3

you have the correct equation that has a period of 3pi/2

now you need to deal with the amplitude and phase shift

Answer 4

y = A*sin(Bx - C) + D


|A| is the amplitude

T = 2pi/B is the period

C/B is the phase shift

y = D is the midline

Answer 5

Oops. I thought I put the amp in, I guess I didn't click the 3 hard enough lol.
y = 3 sin (4/3x-c)

Answer 6

I gotcha, so now you have the equation with the correct period and amplitude

Answer 7

now you just need to deal with the phase shift

Answer 8

(pi/4)/(4/3)?

Answer 9

y = A*sin(Bx - C) + D


|A| is the amplitude

T = 2pi/B is the period

C/B is the phase shift

y = D is the midline

Answer 10

C/B is the phase shift

C is unknown right now
B = 4/3

Answer 11

C/B = pi/4

Answer 12

C/(3pi/2)=pi/4?

Answer 13

B is 4/3, not 3pi/2

Answer 14

Duh...

Answer 15

C/4/3=pi/4

Answer 16

C/(4/3) = pi/4, correct

solve for C

Answer 17

C= pi/3?

Answer 18

A = 3
B = 4/3
C = pi/3
D = 0

Answer 19

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


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


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

Answer 20

D = 0 because by default, the midline is the x axis (when y = 0)

Answer 21

Thank you so much. I get it now. That was confusing.

Answer 22

yeah it's a bit weird and tricky, but you'll get the hang of it all