Write an equation of the cosine function with amplitude 2, period pi, phase shift pi/4.

Question

y=acosx

y=2cos2(x-pi/4)

I got it wrong

Answer 1

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