Question

what would a cosine function look like with an amplitude of 7 period of pie/6 and a vertical shift down of 2

Answer 1

@ganeshie8

Answer 2

▬Sir/Ma'am, A Warm Welcome To Open Study. Sir/Ma'am please show your Working for the question you have posted.▬

Answer 3

@ganeshie8

Answer 4

\[y-A \cos (Bx+C)+D\]
|A| is the amplitude.
The period is
\[T=\frac{2 \pi}{B}\]
The phase shift is
\[\frac{C}{B}\]
and the vertical shift is D.
Can you plug the given values into the above equation?

Answer 5

Sure but can you check if I am correct or not once I do

Answer 6

You will need to find the value of B by solving
\[\frac{2 \pi}{B}=\frac{\pi}{6}\]

Answer 7

what would be B though

Answer 8

like i know i have to solve but do i cross multiply and divide in this case

Answer 9

You can solve in steps:
1. Multiply both sides by B.
2. Multiply both sides of the result by 6/pi.

Answer 10

So for the first step it would look like this 2piB/bb?

Answer 11

Actually just cross-multiplying is easier. Would you like to try that?

Answer 12

Yes please

Answer 13

Would the answer be 2?

Answer 14

Cross-multiplying gives:
\[B \times \pi=12\times \pi\]
Now, divide both sides by pi to find B. Can you do that?

Answer 15

B=12

Answer 16

Good work! So can you now plug the values into the general equation, but omit the phase shift because no phase shift is given in the question?

Answer 17

There is a typo in my general equation. It should be (omitting the phase shift this time):
\[y=A \cos Bx+D\]

Answer 18

A = 7
B = 12
D = -2