Question

find the slope of a tangent line to the parametric curve x(t) = 4t - 4sint, y(t) = 4-4cost when t=pi/4. Use dy/dx = (dy/dt)/(dx/dt)

Answer 1

I got 1 for an answer, if someone could do and check I would appreciate!

Answer 2

x(t) = 4t - 4sint, y(t) = 4-4cost when t=pi/4. Use dy/dx = (dy/dt)/(dx/dt)
Dx(t) = 4 - 4cost
Dy(t)=4sin t
now dy/dx=(dy/dt)/(dx/dt)
=(4sin t)/(4 - 4cost) using t=pi/4
=1+sqrt2

Answer 3

cool can you show work from last step to second to last step

Answer 4

hello

Answer 5

now dy/dx=(dy/dt)/(dx/dt)
=(4sin t)/(4 - 4cost) using t=pi/4
=(4sin (pi/4))/(4 - 4cos(pi/4))
=4(sqrt2/2)/4 - 4(sqrt2/2)))
=2sqrt2/(4-2sqrt2) mult both sides of the eq by (4+2sqrt2)
2sqrt2 (4+2sqrt2)
=----------------------
(4-2sqrt2) (4-2sqrt2)
8sqrt2 +4(2)
=------------
16-4(2)
8sqrt2+8
=---------- dividing by 8 we get
8
=sqrt2+1 ans

Answer 6

any question ivn?

Answer 7

on mult both sides by (4+2sqrt2) youll noticed i made it negative sign,its positive sign,lol

Answer 8

ok nice

Answer 9

ok have fun now, good luck

Answer 10

i have another question reguarding parametrics im about to post oif you could help with that