A curve has equations: x=2sin(t) and y=1-cos(2t). Find dy/dx at the point where t=pi/6

Since this question concerns parametric's, one may move to eliminate t from the equation to calculate dy/dx directly. However, in this case it is much easier to use the chain rule and realise that dy/dx=dy/dt*dt/dx=dy/dt/dx/dt. This is easier as both y and x are very simple to differentiate with respect to t and because the final part of the question involves substituting in a value of t. Differentiating y, the 1 disappears as it is a constant and the -cos(2t) goes to 2sin(2t) using the chain rule. X differentiates to 2cos(t). Using our chain rule from above, dy/dx=2sin(2t)/2cos(t). The 2s cancel. With our knowledge of the double angle formula sin(2t)=2sin(t)cos(t), leaving us with dy/dx=2sin(t)cos(t)/cos(t)=2sin(t). When t=pi/6 dy/dx=2sin(pi/6)=1.