Question

What function accurately represents the sine curve for indigo light?

Answer 1

f(x) = sin 430πx

f(x) = sin 215πx

f(x) = sin pi over 215x

f(x) = sin pi over 430x

Answer 2

430 nm is the wavelength

Answer 3

aka it's the period of that trig function

Answer 4

every 430 nm, it will repeat itself

Answer 5

Period:

T = 2pi/B

430 = 2pi/B

430B = 2pi

B = 2pi/430

B = pi/215

Answer 6

im sorry i dont follow

Answer 7

in general, we have this trig equation

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

Answer 8

the period of that function is T = 2pi/B

Answer 9

T is the period and B is from y = A*sin(Bx - C) + D

Answer 10

So that's why the function is

\[\Large f(x) = \sin\left(\frac{\pi}{215}x\right)\]

Answer 11

ill study your work a bit more so i fully understand, thank you so much, this helped a lot!

Answer 12

you're welcome