Please help me out in this analytic geometry problem?

Question

find the slope of the tangent line to the parametric curve x = 3cost ,y = 4sint at t = ¶/4 and at t = 7¶/4 without eliminating parameter

Answer 1

need to take the derivative vector:
( -3 sin t, 4 cost)
when t= pi/4, the vector is:
(- 3 sin(pi/4), 4 cos(pi/4)) = ( -3/sqrt(2), 4/sqrt(2) )
now, the slope of the tangent line is:
(4/sqrt(2) ) / ( -3/sqrt(2) ) =-4/3
so the equation of the tangent line is:
y- 4sin(pi/4) = -4/3 (x-3cos(pi/4))
y-4/sqrt(2) = -4/3( x-3/sqrt(2) )
'

Answer 2

I am assuming that the symbol you have inserted is Pi. Find the vaue of t and plug in your answers where t is Pi / 4 and 7(Pi / 4), then find the sin and cos of t and multiply by the numbers given.

x = 3(cos(t / Pi)), x = 3(cos(7(Pi / 4)))
y = 4 (sin(t / Pi)), y = 4(sin(7(Pi / 4)))