Trigonometry - Trigonometric Equations
Trigonometry - Trigonometric Equations
The diagram shows a trapezium \(ORST\) inscribed in a circle with centre \(O\) and diameter \(16\) cm. \(OR\) makes an angle \(\theta\), \(0{}^\circ < \theta < 90{}^\circ\), with the diameter of the circle. \(ST\) is perpendicular to both \(RS\) and \(OT\). The perimeter of the trapezium is \(P\) cm.
- Show that \(P = 8 + 24 \cos \theta + 8 \sin \theta\).
- Express \(24 \cos \theta + 8 \sin \theta\) in the form of \(R \cos(\theta - \alpha)\). Hence, find the maximum value of \(P\) and the corresponding value of \(\theta\) at which this value occurs.
- Find the value of \(\theta\) when \(P = 30\) cm.
Video Solution:
Video solution locked
A free account saves your progress; this video needs a course plan.
Solution:
Solution locked
680+ questions here come with free worked solutions. A free account saves your questions and progress; this one needs a course plan.
Create a free account to practise similar questions.
Answer:(a) \(P=8+24\cos\theta+8\sin\theta\) (b) \(24\cos\theta+8\sin\theta=8\sqrt{10}\cos(\theta-18.4^\circ)\), so \(P_{\max}=8+8\sqrt{10}\text{ cm}\) when \(\theta=18.4^\circ\) (c) \(\theta=48.0^\circ\)
Need help? Join our A-Maths tuition classes.
Learn more