The equation of the tangent line to the curve at the point corresponds to the given value of the parameter is
[tex]y - 0 = pi(x + pi)[/tex]
This is further explained below.
Generally, the equation for dx/dt is mathematically given as
dx/dt = cost - tsint
dy/dt = sint + tcost
slope at t =[tex]\pi[/tex]
[tex]slope at t = dy/dx = \frac{[sint + tcost ]}{[cost - tsint ]}[/tex]
[tex]= \frac{[0 - pi]}{[-1] = pi}[/tex]
Given that
[tex]t = \pi,\\ x = -\pi,\\ y = 0[/tex]
[tex]y - 0 = pi(x + pi)[/tex]
In conclusion, The equation of the tangent line to the curve at the point that corresponds to the given value of the parameter is
[tex]y - 0 = pi(x + pi)[/tex]
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