A laser spotlight on a robotic arm traces a path $P\,$ on a high-precision sensor wall. The coordinates $(x, y)$ of the spotlight at time $\theta\,$ are given by the parametric equations

\text{cosec } \theta, \quad y = \cot \left( \theta + \frac{\pi}{6} \right), \quad \frac{\pi}{6} < \theta < \frac{\pi}{2}

Find $dydx\displaystyle \frac{dy}{dx}$ in terms of $θ\theta$ .

Find an equation for the tangent to the path $P\,$ at the point where $θ=π3\displaystyle \theta = \frac{\pi}{3}$ . Give your answer in the form $y = m x + c$ , where $m\,$ and $c\,$ are constants.

Show that all points on the path $P\,$ satisfy the equation

\frac{A x^2 - B\sqrt{x^2 - 1}}{x^2 - C}

where $A$ , $B$ , and $C\,$ are constants to be determined.

A laser spotlight on a robotic arm traces a path $P\,$ on a high-precision sensor wall. The coordinates $(x, y)$ of the spotlight at time $\theta\,$ are given by the parametric equations

\text{cosec } \theta, \quad y = \cot \left( \theta + \frac{\pi}{6} \right), \quad \frac{\pi}{6} < \theta < \frac{\pi}{2}

Find $dydx\displaystyle \frac{dy}{dx}$ in terms of $θ\theta$ .

Find an equation for the tangent to the path $P\,$ at the point where $θ=π3\displaystyle \theta = \frac{\pi}{3}$ . Give your answer in the form $y = m x + c$ , where $m\,$ and $c\,$ are constants.

Show that all points on the path $P\,$ satisfy the equation

\frac{A x^2 - B\sqrt{x^2 - 1}}{x^2 - C}

where $A$ , $B$ , and $C\,$ are constants to be determined.

Differentiation

Question 37

Markscheme

Differentiation

Question 37

Markscheme

Differentiation

Question 37

Differentiation Questions

Differentiation

Question 37

Differentiation Questions