Question

prove that the distance of the point (acos@, asin@) from the origin is always equal to a, whatever be the value of @.

Answer 1

$d = \sqrt{ {(x1 - x2)}^{2} + {(y1 - y2)}^{2} } \\ = \sqrt{ {(a \cos( \alpha ) - 0)}^{2} + {(a \sin( \alpha ) - 0}^{2} } \\ = \sqrt{ {(a \cos( \alpha ) ) }^{2} + {(a \sin( \alpha )) }^{2} } \\ = \sqrt{ {a}^{2} } \\ = a$