SPS
SPS SM Pure
2020
February
— Question 4
5 marks
Exam Board
SPS
Module
SPS SM Pure (SPS SM Pure)
Year
2020
Session
February
Marks
5
Topic
Parametric equations
4
Using \(\sin ^ { 2 } \theta + \cos ^ { 2 } \theta \equiv 1\), show that \(\tan ^ { 2 } \theta + 1 \equiv \sec ^ { 2 } \theta\).
A curve is given parametrically by
$$x = a \sec \theta , \quad y = a \tan \theta$$
where \(a\) is a constant.
Find a Cartesian equation of the curve.
Determine an equation of the tangent to the curve at the point \(\theta = \frac { \pi } { 3 }\), giving your answer in exact form. [0pt]
[5]