Question

Sinusoidal Functions

Answer 1

I need to turn this table into an equation for a sinusoidal function, and I'm lost

Answer 2

I cant figure it out how are we suppost to do this

Answer 3

whats the question

Answer 4

that is the question, turn the table into an equation for a sinusoidal function

Answer 5

consider the general form of a sinusoidal equation \(\large\color{cyan}{y = a ~cos(b(x-c)) + d}\)

Answer 6

you just need to figure out the values of a,b,c and d.

Answer 7

the max value of y would be a+d and min value will be a-d
^ find out a and d from this

Answer 8

b would be \(\large\frac{2\pi}{Time~period}\)

Answer 9

you can find the time period by using the coordinates given for maxima and minima

Answer 10

Btw, use 1,2,3...12 to represent the months

Answer 11

c is essentially the horizontal "shift"
checkout this example: https://www.youtube.com/watch?v=QOCowKoyq_4

Answer 12

Okay step one, how would one find A and D

Answer 13

is the max like, the max number on the table?

Answer 14

we'll be using the x axis to denote the months and the y axis to denote the temperature

Answer 15

\(\color{#0cbb34}{\text{Originally Posted by}}\) @Pixel
is the max like, the max number on the table?
\(\color{#0cbb34}{\text{End of Quote}}\)
yes. the max means the max temperature

Answer 16

so max = 106
Min = 65

Answer 17

and then find two numbers that add up to 106 and subtract to 65?

Answer 18

yup

Answer 19

cos() can take values from between -1 to 1
so if you have something like a cos (b(x-c)) + d, it's max would be when the cos thing goes 1 and min would be when the cos thing goes -1
therefore max = a + d
min = a-d

Answer 20

so what would be the best way of figuring out the two numbers

Answer 21

a+d 106
a-d = 65

Answer 22

https://www.youtube.com/watch?v=QOCowKoyq_4
this is essentially the same question, go through it and you'll probably get your answer

Answer 23

so time period = (7,106), (1,65) = 106-65 = 41 / 2 = 20.5