2020 VJC J1 MYE Q7
2020 VJC J1 MYE Q7
8 marks
Mid Year Exam
A curve \(C\) has parametric equations
\(x=\sin t-\frac{1}{2}t,\) \(y=\cos t,\) for \(0 < t < \pi \)
- Show that the equation of the normal to \(C\) at the point with parameter \(t\) may be expressed as\(y\sin t=\left( \cos t-\frac{1}{2} \right)\left( x+\frac{1}{2}t \right)+\frac{1}{2}\sin t.\)[4]
- Determine the exact coordinates of the points on \(C\) whose normal pass through the point \(\left( -\frac{\pi }{4},\frac{1}{2} \right).\)[4]
Video Solution:
Video solution locked
A free account saves your progress; this video needs tuition enrolment.
Solution:
Solution locked
680+ questions here come with free worked solutions. A free account saves your questions and progress; this one needs tuition enrolment.
Create a free account to practise similar questions.
Answer:\text{(i)}\ \text{shown} \quad \text{(ii)}\ \left(\frac{\sqrt{3}}{2} - \frac{\pi}{6},\; \frac{1}{2}\right) \text{ and } \left(1 - \frac{\pi}{4},\; 0\right)
Need help? Join our JC Math tuition classes.
Learn more