For the parametric equations x = cos(t), y = 3 sin(t), find the equation of the tangent line to the curve at t = 2π/3

Consider the parametric curve C defined by  x = x ( t )  and  y = y ( t ) . (a) Explain how to determine the location of the horizontal tangent line(s) of C.  (b) Explain how to determine the location of the vertical tangent line(s) of C Use complete sentences to answer this question. All math in your solution must be appropriately typeset.

A particle is moving along the curve given by the parametric equations x=tant, y=sect. Find the particle’s speed at t=π6.

Express in terms of "t" for the following parametric equation: x = ln(t); y = sin² (t) and evaluate it when t = 8.1. Give your answer to 3 decimal places. Note that t is in radians.