Own-Cupcake7586 t1_j6eguj8 wrote
If you don’t put a multiplier ahead of the sin and cos terms, they always fall on a scale of -1 to 1. The equation you wrote is concerned only with the angles. None of those terms relate to radius.
321ECRAB123 t1_j6ehfb7 wrote
Isnt the 1 supposed to represent the hypotanuse? What if its not 1? Will the equation still work?
LordEarArse t1_j6eich5 wrote
If you change one side of an equation you have to make exactly the same change to the other side for the equation to remain equal.
Own-Cupcake7586 t1_j6eidx7 wrote
One is the default for the functions. If you’re looking for the output to be a length, you need to scale them accordingly. For example, for a circle of radius 3, you’d write:
3 x (sin^2 + cos^2 ) = 3(x1)
The definition of the equation stays the same, but both sides get scaled evenly.
Hope that helps.
RootedPopcorn t1_j6eiydy wrote
If the hypotenuse is not 1, then the x and y sides will not be sine and cosine, but rather a scaled version of them.
Remember that sine and cosine represent ratios, so if the hypotenuse is r, then (x,y)=(rsin(a), rcos(a)), where 'a' is the angle. By pythagorian theorem, x^(2) + y^(2) = r^(2), note that 'r' can be divided on both sides to make the right side 1.
Chromotron t1_j6et2iu wrote
No, the 1 is to represent 1 and nothing else. It comes from the definition of sin and cos in the unit circle.
Viewing a single comment thread. View all comments