Maths · Fundamentals of trigonometry. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.
An angle can be measured in two systems. The sexagesimal system uses degrees, minutes and seconds. The circular system uses the radian: the angle at the centre of a circle made by an arc equal in length to the radius. A full turn is 360° or 2π radians.
Radians make the formulas for arc length and sector area very simple, but the angle must be in radians before you use them.
An angle is in standard position when its vertex is at the origin and its initial side lies along the positive x-axis. Anticlockwise turning is positive. Coterminal angles finish on the same terminal side. A quadrantal angle has its terminal side on an axis.
Putting an angle in degrees into l = rθ or A = ½r2θ. Change the angle to radians first.
Answer: Arc length 2π cm (about 6.28 cm); area 8π cm2 (about 25.1 cm2).
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