Trigonometric functions and circular measure - the Australian ...

{32} • Trigonometric functions and circular measureExampleIn a circle of radius 36 cm, find the area of a sector subtending an angle of 30 ◦ at thecentre.SolutionO30 º36 cmWith r = 36 and θ = 30 ◦ = π , we have6A = 1 2 × 362 × π 6 = 108π cm2 .As mentioned above, in problems such as these it is best to leave your answer in termsof π unless otherwise stated.The area A s of a segment of a circle is easily found by taking the difference of two areas.OθrIn a circle of radius r , consider a segment that subtends an angle θ at the centre. We canfind the area of the segment by subtracting the area of the triangle (using 1 2ab sinθ) fromthe area of the sector. ThusA s = 1 2 r 2 θ − 1 2 r 2 sinθ = 1 2 r 2 (θ − sinθ).