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All 8 Flashcards — Radian measure, arcs & sectors
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Question
What is one radian?
Answer
The angle at the centre of a circle subtended by an arc equal in length to the radius (≈ 57.3°).
Question
Convert degrees to radians.
Answer
Multiply by π/180 (since π rad = 180°).
Question
Convert radians to degrees.
Answer
Multiply by 180/π.
Question
How many radians in a full turn?
Answer
2π radians = 360° (and π radians = 180°).
Question
Arc-length formula?
Answer
l = rθ, with θ in radians.
Question
Sector-area formula?
Answer
A = ½r²θ, with θ in radians.
Question
Express 60° in radians.
Answer
60 × π/180 = π/3 radians.
Question
Why must θ be in radians for l = rθ and A = ½r²θ?
Answer
The formulas come from the fraction θ/(2π) of the circle; the 2π only cancels cleanly when θ is measured in radians.
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Full study notes for Radian measure, arcs & sectors
Topic 3.7 hub
Radians (HL only)
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