A robotic arm is programmed to sweep across a linear welding track. Its horizontal position xxx (in cm) relative to a central sensor is modeled by the equation
x=5tan(y−π4)x∈R,−π4<y<3π4x = 5\tan\left(y - \frac{\pi}{4}\right) \quad x \in \mathbb{R}, \quad -\frac{\pi}{4} < y < \frac{3\pi}{4}x=5tan(y−4π)x∈R,−4π<y<43π
where y y\,y is the angle of rotation of the arm in radians.
Show that
dydx=ax2+b\frac{dy}{dx} = \frac{a}{x^2 + b}dxdy=x2+ba
where a a\,a and b b\,b are integers to be found.
The point P P\,P on the curve C C\,C has yyy-coordinate π2\displaystyle \frac{\pi}{2}2π. The tangent to C C\,C at P P\,P crosses the xxx-axis at the point QQQ. Find the exact xxx-coordinate of QQQ.
Practise Edexcel A Level Maths 9.7 Parametric Differentiation with exam-style questions for A Level Maths. 36 questions, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.