Write an equation of the cosine function with amplitude 2, period pi, phase shift pi/4.
y=acosx
y=2cos2(x-pi/4)
I got it wrong
The general equation of such cosine function is:y=acos(x-phasedifference),
y=displacement
a=amplitude
x=angular displacement
=(angular velocity)*time
=(2pi/time period)*time
Therefore, the equation can be written as: y=2cos[x-(pi/4)]..........(a)
or,y=2cos[(2pi/pi)*t-(pi/4)]
or,y=2cos[2t-(pi/4)].........(b)
where t=time
Mathematically, equation (a) is suitable
Physically, equation (b) is suitable
To write the equation of a cosine function with the given characteristics, you can start with the general formula:
y = A * cos(B * (x - C))
Where:
- A represents the amplitude.
- B represents the frequency. It is related to the period T by B = 2π / T.
- C represents the phase shift.
Given that the amplitude (A) is 2, the period (T) is π, and the phase shift (C) is π/4, let's substitute these values into the equation:
A = 2
T = π
C = π/4
B = 2π / T = 2π / π = 2
Replacing A, B, and C in the general formula, the equation becomes:
y = 2 * cos(2 * (x - π/4))
So, the correct equation is y = 2 cos(2x - π/2).