find the radius of the curvature at (acostheta^3,asintheta^3) on the curve x^2/3+y^2/3=a^2/3
radius of the curvature:
"R=\\frac{(1+(dy\/dx)^2)^{3\/2}}{|d^2y\/dx^2|}"
"2x\/3+2yy'\/3=0"
"y'=-\\frac{x}{y}"
"y''=-\\frac{y-xy'}{y^2}"
at point "(acos \\theta^3 ,asin \\theta ^3):"
"y'=-cot\\theta^3"
"y''=-\\frac{sin\\theta^3-cos^2\\theta^3\/sin\\theta^3}{sin^2\\theta ^3}"
"R=\\frac{sin^2\\theta ^3(1+cot^2\\theta^3)^{3\/2}}{sin\\theta^3-cos^2\\theta^3\/sin\\theta^3}"
Comments
Leave a comment