Question

In the diagram, the y-coordinate of each edge illustrates a cosine function. Write an equation for the y-coordinate of one edge. (Diagram attached)

Answer 1

the equation for a cosine function is y = A*cos(Bx) where A affects the amplitude (height of the wave) and B affects the period of the wave (the places it crosses the x-axis)

The amplitude (highest and lowest values of the curve) of a regular cosine function is 1...which you have (the curve goes from -1 to 1) so A = 1.

Normally, the curve will cross the x-axis at pi/2 and 3pi/2, but here it crosses at 6 and 18.

So, to find B, we need to solve B(pi/2) = 6...multiply both sides by pi/2 and you'll have B.

Your answer will be y = cos(Bx) where B is the answer you get from that solution...the other curve would be the same with a negative in front.

Answer 2

SO B = 9.42 ?

Answer 3

doesn't look right...best to leave it in terms of pi.

B(pi/2) = 6
B = 6(2/pi)
B = 12/pi

You can check this against the 3pi/2...B(3pi/2) should equal 18

(3pi/2)(12/pi) = 36pi/2pi = 18 since the pis cancel top/bottom, and a 2 cancels top/bottom.

makes sense?

Answer 4

Oh okay, yes, makes a lot more sense now!

Answer 5

The equation would be y = cos (12/pi) Correct?

Answer 6

Or is it y = cos (12/pi) x

Answer 7

\[y=\cos(\frac{ 12 }{ \pi }x)\]