Question

Can someone explain how to do these two problems?

http://gyazo.com/4b47d52f7388f9eee2ea59b65aa0a655

Answer 1

I am sorry for my answers last night.. :)
now I compensate :
for \(y = 4 sin(\theta/2 +\pi)-1= 4 sin ((1/2)\theta +\pi) -1\)
your k = 1/2
your \(c=\pi\)
hence the phaseshift is \(-\dfrac{c}{k}=\dfrac{-\pi}{1/2}= - 2\pi\) the negative sign shows the graph moves to the right.

Answer 2

for \(y = 4 sin(\dfrac{\theta}{4}-\dfrac{\pi}{4})-2\)
your c is \(c = \dfrac{-\pi}{4}\)
your k is 1/4
hence the phaseshift: \(\dfrac{\dfrac{-\pi}{4}}{\dfrac{1}{4}}=-\pi\)

Answer 3

again, negative sign shows the graph is shifted to the right

Answer 4

What about for the original question? http://gyazo.com/4b47d52f7388f9eee2ea59b65aa0a655 @Loser66

Answer 5

\(y= 2sin(2x-pi/2)+3 \)

Answer 6

Can you show how you got that?

Answer 7

Is it the same process for #14?

Answer 8

we have formula to do, right? it say \(y =\pm Asin(kx +c) + verticalshift\)
and PS = -c/k,

Answer 9

A is amplitude, nothing to do with it, just put 2 there, ok?

Answer 10

Okay

Answer 11

k has formula , that is period = 2pi/ number in the front of x = \(\dfrac{2pi}{k}\)

Answer 12

hence \(period= \dfrac{2pi}{k}\\k= \dfrac{2pi}{period}\)

Answer 13

given period is pi, hence k = 2 , ok?

Answer 14

Now, so far, wy have y =2 sin(2x +c) + 3 ( 3 is vertical shift)

Answer 15

so , remain is c
PS = -c/k.
given PS = pi/4, k =2 as above, then c = -PS*k = - (pi/4)*2 =-pi/2

Answer 16

Combine all, y = 2 sin(2x -pi/2) +3

Answer 17

Take time to digest, I go for dinner.

Answer 18

Is that the same process for number 14? @Loser66

Answer 19

Cause that one is sin, but #14 is cos

Answer 20

yup, cos and sin are the same

Answer 21

What if it was tan or something?

Answer 22

tan is another topic.

Answer 23

it doesn't have amplitude,

Answer 24

Okay, thanks for clearing that up for me. @Loser66 I will show you my work for #14 and tell me if it's right when you get back. Enjoy your dinner.

Answer 25

it doesn't have phaseshift or vertical shift.

Answer 26

Pi/2= 2pi/k
K= 4
C= -ps*k = -(-pi)*4
C=4pi

Y=1/2cos(4theta+4pi)-7