Maths: Analysis and Approaches · Geometry and trigonometry. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.
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A radian is another unit for angles. One full turn is 2π radians, so π radians = 180°. With angles in radians, the formulas for arc length and sector area become very short.
The unit circle has radius 1 and centre at the origin. If a radius makes an angle θ with the positive x-axis, the point at its end is (cos θ, sin θ). This defines sine and cosine for any angle and shows their signs in each quadrant.
You must know the exact values for 0, π/6, π/4, π/3 and π/2. For a multiple such as 5π/4, use the related acute angle and the sign for that quadrant. When the sine rule gives sin C, there may be two possible angles: C and 180° − C.
Students use l = rθ or A = ½r2θ with the angle in degrees. Convert the angle to radians first, and remember that the perimeter of a sector is the arc plus two radii.
Answer: Area = 12 cm2 and perimeter = 14 cm.
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