eliminate the parameter t from the following
x = 9sin t y = 9cos t
Is "y" part of the number you are taking the sine of? In other words, do you mean sin(ty) or siny * t ?
To eliminate the parameter t from the equations x = 9sin t and y = 9cos t, we can use the Pythagorean identity sin^2 t + cos^2 t = 1.
First, square both equations to get:
x^2 = (9sin t)^2 = 81sin^2 t
y^2 = (9cos t)^2 = 81cos^2 t
Next, substitute sin^2 t with 1 - cos^2 t (using the Pythagorean identity) in the first equation:
x^2 = 81(1 - cos^2 t)
Now, isolate cos^2 t:
cos^2 t = 1 - (x^2 / 81)
Finally, substitute cos^2 t in the second equation with the above expression:
y^2 = 81(1 - (x^2 / 81))
Simplifying the equation further:
y^2 = 81 - x^2
Taking the square root on both sides, we get:
y = ±√(81 - x^2)
So, by eliminating the parameter t, the equation relating x and y becomes:
y = ±√(81 - x^2)