Were you given restrictions on ? Because for , y' cannot be expressed as a function of x' (since it fails the vertical line test).
I have a sinusoid curve in an euclidian orthonormal plane [OX,OY].
the equation of the curve is y=a sin x.
Now, I want to get the equation of the curve when I rotate it by an angle with respect to the (ox) axis like it is shown in the figure submitted.
To do that,I'll define tehe vectorial euclidian rotation :in an oriented vectorial euclidian plan, a vectorial rotation is simply defined by its angle . Its matrix in an orthonormal direct basis is :
In another way, a vector (x,y) has as image the vector (x',y') that can be calculated like that :
then we have :
as we have
, then we have
the problem is that I must write in function of .
Thank you for reading me. I'll be vey glad if you can help me
thank you for answering but I didn't understand why I must give restrictions to ?
I tried to solve the problem like that but It seems to me complicated:
As we have y=a sin x.
and if we rotate the vector v(x',y') in an angle -, we have then u(x,y) and the matrix of rotation is:
then we have
then we replace x and y in the equation y=a sin x by their expressions in funtion of x' and y'.
we then have:
The problm now is how to write the equation in a simple form y'=f(x').
Could you help me.