Main Question or Discussion Point
stupid question from a high school kid. How do you algebraically rotate (not flip) a function about the origin for any given angle? and what is the notation for it?
Nothing stupid about that question.stupid question from a high school kid. How do you algebraically rotate (not flip) a function about the origin for any given angle? and what is the notation for it?
Sort of.so you mean for y=f(x) you can get the new function by plugging f(x) for y into the matrices and multiplying them?
I get first row: x cos(theta) - f(x) sin(theta)
second row: f(x) cos(theta) + x sin(theta)
Is the new function f(x) cos(theta) + x sin(theta)?
Okay, so your function is y = e^x, right? If you plug in a specific value of x, say 1.5, then you get y = e^1.5 = 4.5 (approximately).I tried putting e^x cos(pi/3) + x sin(pi/3) on my calculator and it didn't work. Am I doing something wrong?
If your original function is y= f(x), you can use x itself a parameter: x= t, y= f(t).i have a ti-83... what do i put in X1T and Y1T?
Not in general, I wouldn't think. Suppose you rotate a sine curve by more than 45 degrees - it will no longer be single-valued, so you won't be able to write down a simple expression for the resulting function. If it is in closed form, I'll bet it's ugly!the most important for me is the functional form. is it in closed form?