Question

find the tangent line equation at x=cost+sin2t, y=sint+cos2t, t=0

Answer 1

y = sin t + cos^2 t - sin^2 t
dy/dt = cos t -2cost sint -2 sint cost
at t = 0 dy/dt = 1

x = cos t +2 sin t cos t
dx/dt = -sint -2sin^2t+2 cos^2t
at t = 0 dx/dt = 2

dy/dt / dx/dt = 1/2 = slope

x = 1 and y = 1 at t = 0
y = 1 x + b
b = 0
y = x

Answer 2

x = 1 and y = 1 at t = 0
y = .5 x + b
1 = .5 + b
b = .5
y = .5 x + .5

Answer 3

the 2s aren't exponents, is the process the same?