Trigonometry and Circular Measure
GCE Further Mathematics

a) A sector of a circle has an area of 75 cm² and a perimeter of 40 cm. Find: i) the radius of the circle, ii) the angle subtended at the centre of the circle in radians, iii) the length of t…

a) Prove the identity: (cos θ)/(1 - sin θ) - (cos θ)/(1 + sin θ) = 2 tan θ. b) i) Express 3 sin x + 4 cos x in the form R sin(x + α), where R > 0 and 0° < α < 90°. State the values of R and α correct…

Find the value of $\cos 300°$.

A sector of a circle has radius 9 cm and an arc length of 6 cm. Find the area of the sector.

If $\sin\theta = \frac{5}{13}$ and $\theta$ is acute, find the value of $\tan\theta$.

Simplify $\frac{\sin 2\theta}{1 + \cos 2\theta}$.

Solve for $\theta$ in the range $0° \leq \theta \leq 360°$: $2\cos^2\theta - \cos\theta - 1 = 0$.

Solve for $\theta$ in the range $0° \leq \theta \leq 360°$: $2\cos^2\theta - \cos\theta - 1 = 0$.

The expression $\sin(A + B) - \sin(A - B)$ simplifies to:

A chord of a circle of radius 10 cm subtends an angle of $\frac{2\pi}{3}$ radians at the centre. Find the length of the chord.

Convert 210° to radians, leaving your answer in terms of π.