Question

x= a(cost+tsint), y=a(sint-tcost), find the value of dy/dx when t= 540°/4​

Answer 1

Answer:

Given: x=a(cost+ tsint) & -------- (1)

y = a(sint-tcost) ------------(2)

t= 540/4

Now,

differentiate eq (1) with respect to x

==> a(-sint + tcost + sint)

==>a ( tcost)

differentiate eq(2) with respect to y

==> a(cost - (-tsint + cost)

==> a(cost + tsint - cost)

==> a(tsint)

by using parametric form

dy/dx = dy/dt/dx/dt

= a(tsint)/a(tcost)

dy/dx = sint/cost

then t = 540/4 =135

dy/dx = sin(135)/cos(135)

= 0.7071/(-0.7071)

= -1