math help!?

Question

wat is the equation of a sine wave along the Y=X line?

i mean sine wave about the Y=X line

Answer 1

If you start with the sine wave on the x- axis, the equation is y = A sin w*x

Then apply a coordinate rotation at ø = 45º. The formula for coordinate rotation is

x' = x*cosø - y*sinø

y' = x*sinø + y•sinø

for ø = 45º, sinø = cosø = √2 / 2

x' = x*√2 / 2 - y*√2 / 2

y' = x*√2 / 2 + y•√2 / 2

put in y = A*sin w*x

x' = (√2 / 2)*[x - A*sin w*x]

y' = (√2 / 2)*[x + A*sin w*x]

x now becomes a parameter in the equations for x' and y', so that the general equations for a sine wave along a 45º line may be written

x(t) = (√2 / 2)*[t - A*sin w*t]

y(t) = (√2 / 2)*[t + A*sin w*t]


with t as the parameter.