Question

Find an equation of a sine function with an amplitude of 2, a period of pi and a y-intercept of -4.

Answer 1

Can i get help please?

Answer 2

@phi

Answer 3

\[ y = A \sin\left(\frac{2 \pi}{T} x + B\right) \]

A is the amplitude
T is the period
we still have to figure out B

Answer 4

This is what I have so far
Y=4 sin 2(x)

Answer 5

oh, I was thinking we needed to include a phase shift B
but it looks like we need an offset, so let's use
\[ y = 2 \sin 2x+ B\]

Answer 6

Yes

Answer 7

I need help finding b

Answer 8

amplitude is 2 (they tell us this, so we have to use 2, not 4)
to find the offset, we use this info:
y-intercept of -4.
that means the point (0, -4)
use x=0 and y= -4 and solve for the offset.

Answer 9

Nvm the amolitude is 2

Answer 10

yes,
y = 2 sin(2x) + B

to find B, set x=0 and y= -4
-4 = 2 sin(2*0)+B
-4 = 2*0+B
-4 = B

Answer 11

So y=2 sin pi(x)?

Answer 12

that has the correct amplitude, but not the correct period
nor the correct offset.

Answer 13

So how do you fidn the period

Answer 14

\[ y = A \sin\left(\frac{2 \pi}{T} x \right)+B\]

if you know T, plug it in and simplify

if you have , for example sin(x) which is sin(1*x)
then 2pi/T = 1 (the number in front of the x)
and solve for T to get T= 2pi. in other words, sin(x) has a period of 2pi

Answer 15

So y=2sin2pi(x)-4?

Answer 16

almost. they say T=2
plug in T=2 into 2pi/T to get the number in front of the x

Answer 17

*T = pi (not 2)

Answer 18

2?

Answer 19

yes

Answer 20

So it would be y= 2 sin 2(x)-4?

Answer 21

The equation

Answer 22

I would write it as
y= 2 sin(2x) - 4

Answer 23

Ok thanks!

Answer 24

So if i had a similar problem but they gave me a phase shift instead if y intercept, how would I find B?

Answer 25

@phi