Question

A cos wave has its first maximum at the point (pie/2, 2) and its first minimum at (5pie/2, -4) what is the equation of the function?

I remember writing 3cos(1/2(x-pie/2)-1 but I'm sure that it's wrong ?

Answer 1

well it ranges from -4 to +2
-4 to 2 = 6
so you are right the amplitude is 3

y = 3 cos (a x - phi)

when x = pi/2 , cos (a x - phi) = 1
so
a pi/2 - phi = 0 because cos 0 = 1

when x = 5 pi/2, cos ( a x- phi) = -1
so
a 5 pi/2 - phi = pi, because cos pi = -1
so we have two equations for a and phi
a pi/2 - phi = 0
a 5 pi/2 - phi = pi
---------------------- subtract
a * -4 pi/2 = -pi

2 a = 1
a = 1/2
phi = 1/2 * pi/2 = pi/4
so I get
3 cos (2x - pi/4)

Answer 2

3 cos (x/2 - pi/4)

That is very close to what you have except for that strange -1 at the end.

Answer 3

yes, you need that -1 at the end

Answer 4

So is my equation correct?

Answer 5

yes, it is correct

except that the Greek letter is <u>pi</u> <b>not</b> <u>pie</u>!!