![]() Therefore the equation for the spiral becomes r = k θ. In particular, d ( P, O ) = r, d ( P, O ) = r, and θ θ is the second coordinate. However, if we use polar coordinates, the equation becomes much simpler. Īlthough this equation describes the spiral, it is not possible to solve it directly for either x or y. d ( P, O ) = k θ ( x − 0 ) 2 + ( y − 0 ) 2 = k arctan ( y x ) x 2 + y 2 = k arctan ( y x ) arctan ( y x ) = x 2 + y 2 k y = x tan ( x 2 + y 2 k ). Next use the formulasĭ ( P, O ) = k θ ( x − 0 ) 2 + ( y − 0 ) 2 = k arctan ( y x ) x 2 + y 2 = k arctan ( y x ) arctan ( y x ) = x 2 + y 2 k y = x tan ( x 2 + y 2 k ). This leads to r 2 = 6 r cos θ − 8 r sin θ. Multiply both sides of the equation by r.However, in this case we do not introduce new points. ![]() ![]() This should always be taken into consideration. ( Note: when squaring both sides of an equation it is possible to introduce new points unintentionally. In general, any polar equation of the form r = k r = k where k is a positive constant represents a circle of radius k centered at the origin. This gives the equation x 2 + y 2 = 9, x 2 + y 2 = 9, which is the equation of a circle centered at the origin with radius 3.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |