curve C with parametric equations x = 4 tan(t), y=5*3^(1/2)*sin(2t). Point P lies on C with coordinates (4*3^(1/2), 15/2). Find the exact value of dy/dx at the point P.
dy/dx = dy/dt *dt/dx (chain rule).
x=4tan(t) hence dx/dt = 4 sec2(t)
y = 531/2sin(2t) hence y'= 1031/2 cos(2t)
therefore dy/dx = 1031/2 cos(2t) / 4sec2(t). Since P is on point with x=431/2 we can duduce that t=π/3 and substituting t in dy/dx we get -531/2/16
HP
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