Question

N1. найти у' и у" x=3(t-sint) y=3(1-cost) n2. найти у' tgy=4y-5x

Answer 1

$1)\quad \left \{ {{x=3(t-sint)} \atop {y=3(1-cost)}} \right.\\\\y'_{x}= \frac{3sint}{3(1-cost)} = \frac{2sin\frac{t}{2}\cdot cos\frac{t}{2}}{2sin^2\frac{t}{2}} =ctg\frac{t}{2}\\\\y''_{x}= \frac{-\frac{1/2}{sin^2\frac{t}{2}}}{3sin^2\frac{t}{2}} =- \frac{1}{4sin^4\frac{t}{2}} \\\\2)\quad tgy=4y-5x\\\\\frac{y'}{cos^2y}=4y'-5\\\\y'(4-\frac{1}{cos^2y})=5\\\\y'= \frac{5}{4-\frac{1}{cos^2y}} =\frac{5cos^2y}{4cos^2y-1}$