A curve has the parametric equations
x=tan2t,y=cost,0<t<π2 x = \tan^2 t, \quad y = \cos t, \quad 0 < t < \frac{\pi}{2} x=tan2t,y=cost,0<t<2πFind an expression for dydx\displaystyle \frac{dy}{dx}dxdy in terms of ttt.
Find an equation of the tangent to the curve when t=π4\displaystyle t = \frac{\pi}{4}t=4π
Show that a cartesian equation for the curve is
y2=11+x y^2 = \frac{1}{1+x} y2=1+x1Hence state the range of possible values of xxx.
215 exam-style questions on Edexcel A Level Maths Parametric Equations, covering 8.1 Parametric Equations, 8.2 Using Trigonometric Identities, 8.3 Curve Sketching, 8.4 Points of Intersection, and 8.5 Modelling with Parametric Equations. Each one has a worked solution and a mark scheme showing where the marks go.