2 interactive labs · AS & A Level Mathematics 9709
Radians and Arc Length: s = rθ
1.4 Circular measure · Lay the radius along the arc to see a radian, then use s = rθ to find the arc, the angle or the radius, and convert between degrees and radians.
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About this lab
Lay the radius along the arc to see a radian, then use s = rθ to find the arc, the angle or the radius, and convert between degrees and radians.
You will be able to
Explain that one radian is the angle at the centre subtended by an arc equal to the radius, so θ = s ÷ r, and state that 180° = π radians.
Convert between degrees and radians, giving exact multiples of π (or decimals to 3 s.f.) and angles in degrees to 1 d.p.
Calculate the arc length s = rθ, and rearrange it to find θ = s ÷ r or r = s ÷ θ, with θ in radians and 0 < θ ≤ 2π.
Sector, Triangle and Segment
1.4 Circular measure · Choose a sector, a segment or an arc-and-tangent region, set r and θ in radians, predict its area or perimeter, then check the working.
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About this lab
Choose a sector, a segment or an arc-and-tangent region, set r and θ in radians, predict its area or perimeter, then check the working.
You will be able to
Calculate the area of a sector, A = ½r²θ, and its perimeter 2r + rθ, with θ in radians and 0 < θ ≤ 2π.
Find the chord AB = 2r sin(θ/2), the triangle area ½r² sin θ and the area of a segment as the sector minus the triangle, ½r²(θ − sin θ).
Determine the area and perimeter of a region bounded by an arc, a tangent and a radius extended, using right-angled triangle trigonometry.
Give exact answers in terms of π and surds where they exist, with the 3 s.f. value beside them, and explain why the calculator must be in radian mode.
