Radians, arcs & sectors
Practice Flashcards
What is one radian?
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All Flashcards in Topic 3.4
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3.4.19 cards
What is one radian?
The angle at the centre of a circle whose arc length equals the radius.
How many radians in a full circle?
2π (and π in a half circle, 180°).
Convert degrees to radians?
Multiply by π/180.
Convert radians to degrees?
Multiply by 180/π.
Radian values of 30°, 45°, 60°, 90°?
π/6, π/4, π/3, π/2.
60° in radians?
60 × π/180 = π/3.
3π/4 radians in degrees?
3π/4 × 180/π = 135°.
Why must the GDC mode match?
sin/cos of a radian angle need radian mode; a mode mismatch gives wrong values.
Which mode does calculus with sin/cos use?
Radians.
3.4.29 cards
Arc length formula?
s = rθ, with θ in radians.
Sector area formula?
A = ½r²θ, with θ in radians.
What must θ be in for these formulas?
Radians — convert from degrees first if needed.
How do you find the angle from arc and radius?
θ = s/r.
Perimeter of a sector?
Arc + two radii = rθ + 2r.
Area of a segment?
Sector area minus triangle area: ½r²θ − ½r²sinθ.
Area of the triangle between two radii?
½r²sinθ (two sides r, included angle θ).
Sector radius 6, angle 1.5 rad — area?
½(36)(1.5) = 27.
Sector radius 5, arc 15 — angle?
θ = 15/5 = 3 radians.
Topic 3.4 study notes
Full notes & explanations for Radians, arcs & sectors
Math AA SL exam skills
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