Question

find the equation of the evolute of the curve x=a(cost+tsint),y=a(sint-tcost)​

Answer 1

at is the equation of the evolute, at the point 't'.

Given:

x= a(cost+tsint),

y= a(sint-tcost)​

To find:

The equation of the evolute of the curve

Solution:

x' (derivative of x w.r. to t)

= a(-sint + sint + t cost)

= at cost

y' (derivative of y w.r. to t)

= a (cost-cost + t sint)

= at sint

Similarly,

x" (derivative of x' w.r. to t)

= a (cost -t sint)

y" (derivative of y' w.r. to t)

= a (sint + t cost)

⇒ radius of curvature (p)

= (x²+y2)3/2 / x'y' - y'x

= {a^2t^2(sin^2 t+cos^2 t)}3/2 / a²(t sint cost+t-cost-t sint cost+t-sin-t)

= a^3t^3 / a^2t^2(cos^2t+sin^2t)

=at

= at is the equation of the evolute, at the point 't'.

#SPJ1

Answer 2

Step-by-step explanation:

step by step explanation need