Примеры графиков параметрических функций на плоскости

\[ x = \sin(t), \quad y = \cos(t), \quad t \in [0; 2\pi] \]

\[ x = t \sin(t), \quad y = t \cos(t), \quad t \in [0; 5\pi] \]

\[ x = 2\cos(t) + \cos(2t), \quad y = 2\sin(t) - \sin(2t), \quad t \in [0; 2\pi] \]

\[ x = 2\sin^{3}(t), \quad y = 2\cos^{3}(t), \quad t \in [0; 2\pi] \]

\[ x = 20\Big(\cos(t) + \frac{\cos(5t)}{5}\Big), \quad y = 20\Big(\sin(t) - \frac{\sin(5t)}{5}\Big), \quad t \in [0; 2\pi] \]

\[ x = 4,4\Big(\cos(t) + \frac{\cos(1,1t)}{1,1}\Big), \quad y = 4,4\Big(\sin(t) - \frac{\sin(1,1t)}{1,1}\Big) \\ t \in [0; 20\pi] \]

\[ x = 24,8\Big(\cos(t) + \frac{\cos(6,2t)}{6,2}\Big), \quad y = 24,8\Big(\sin(t) - \frac{\sin(6,2t)}{6,2}\Big) \\ t \in [0; 10\pi] \]

\[ x = \Big(1 + \cos(t)\Big)\cos(t), \quad y = \Big(1 + \cos(t)\Big)\sin(t), \quad t \in [0; 2\pi] \]

\[ x = 6\cos(t) - 4\cos^3(t), \quad y = 4\sin^3(t), \quad t \in [0; 2\pi] \]

\[ x = 8\Big(\cos(t) - \frac{\cos(4t)}{4}\Big), \quad y = 8\Big(\sin(t) - \frac{\sin(4t)}{4}\Big), \quad t \in [0; 2\pi] \]

\[ x = 6,2\Big(\cos(t) - \frac{\cos(3,1t)}{3,1}\Big), \quad y = 6,2\Big(\sin(t) - \frac{\sin(3,1t)}{3,1}\Big) \\ t \in [0; 20\pi] \]

\[ x = 13\Big(\cos(t) - \frac{\cos(6,5t)}{6,5}\Big), \quad y = 13\Big(\sin(t) - \frac{\sin(6,5t)}{6,5}\Big) \\ t \in [0; 4\pi] \]

\[ x = \sin(t)\bigg(\mathrm{e}^{\cos(t)} - 2\cos(4t) + \sin^5\Big(\frac{1}{12}t\Big)\bigg) \\ y = \cos(t)\bigg(\mathrm{e}^{\cos(t)} - 2\cos(4t) + \sin^5\Big(\frac{1}{12}t\Big)\bigg) \\ t \in [0; 12\pi] \]

\[ x(t) = \sin\Big(t + \frac{\pi}{2}\Big), \quad y(t) = \sin(2t), \quad t \in [0; 2\pi] \]

\[ x(t) = \sin\Big(3t + \frac{\pi}{2}\Big), \quad y(t) = \sin(2t), \quad t \in [0; 2\pi] \]

\[ x(t) = \sin\Big(5t + \frac{\pi}{2}\Big), \quad y(t) = \sin(6t), \quad t \in [0; 2\pi] \]

\[ x(t) = 16\sin^3(t) \\ y(t) = 13\cos(t) - 5\cos(2t) - 2\cos(3t) - \cos(4t) \\ t \in [0; 2\pi] \]