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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.

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321ECRAB123 t1_j6ehfb7 wrote

Isnt the 1 supposed to represent the hypotanuse? What if its not 1? Will the equation still work?

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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.

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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.

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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.

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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.

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