Circular Measure

You will be able to

• Define a radian as the angle at the centre subtended by an arc equal in length to the radius, and explain why a full turn is 2π radians.
• Convert between degrees and radians using π radians = 180°, giving exact answers such as 135° = 3π/4.
• State that 1 radian ≈ 57.3° and give an angle in radians to 3 significant figures.

You will be able to

• Calculate the arc length s = rθ and the sector area A = ½r²θ, with θ in radians, giving exact answers in terms of π where θ is a multiple of π.
• Calculate the area of a segment as ½r²(θ − sin θ) and the perimeter of a sector or segment, using 2r sin(θ/2) for the chord.
• Solve problems on composite shaded regions, and find r or θ from a given arc length or area.