Mathematics 7357: Trigonometry Topical Past Paper Questions

The diagram below shows a sector of a circle OAB. The chord AB divides the sector into a triangle and a shaded segment. Angle AOB is $\frac{\pi}{6}$ radians. The radius of the sector is 18 cm. Show that the area of the shaded segment is $$ k(\pi-3)cm^{2} $$ where k is an integer…

(a) Given that $\cos\theta\neq\pm1$, prove the identity $$ \frac{1}{1-\cos\theta}+\frac{1}{1+\cos\theta}\equiv2\operatorname{c o s e c}^{2}\theta $$ 1 - COS U 1 + COS U [4 marks] (b) Hence, find the set of values of $A$ for which the equation $$ \frac{1}{1-\cos\theta}+\frac{1}{1+…

(a) Sketch the graph of $$ y=\sin2x $$ [2 marks] (b) The equation $$ \sin2x=A $$ has exactly two solutions for $ 0^{\circ} \leq x \leq 360^{\circ} $ State the possible values of $A$. [1 mark] _____