Trigonometry (A2 Unit 3: Pure Mathematics B) — WJEC A-Level Mathematics
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Trigonometry (A2 Unit 3: Pure Mathematics B) explained
A radian is the angle subtended at the centre of a circle by an arc whose length equals the radius.
Read the full explanation
Consequently, a complete revolution of 360° equals 2π radians, giving π radians = 180°. Radians simplify circular formulas: the arc length of a circle of radius r subtending angle θ is s = rθ; the area of a sector is Area_sector = ½r²θ. The area of a circular segment is found by subtracting the area of the isosceles triangle formed by the radii and chord (Area_triangle = ½r² sin θ) from the sector area: Area_segment = ½r²θ − ½r² sin θ = ½r²(θ − sin θ). When solving problems combining sector areas and segments, the angle θ must always be expressed in radians, and calculators must be kept in radian mode throughout.
Your focus
- Convert angles fluently between degrees and radians.
- Calculate arc lengths and sector areas using s = rθ and Area = ½r²θ.
- Calculate areas of circular segments using Area = ½r²(θ − sin θ).
Trigonometry (A2 Unit 3: Pure Mathematics B) exam tips
Marking Points
- calculating arc length using s = rθ with θ in radians
- calculating sector area using Area = ½r²θ with θ in radians
- subtracting triangle area ½r² sin θ from sector area to find segment area
- converting between degrees and radians using the equivalence π radians = 180°
Examiner Tips
- 💡Ensure your calculator displays 'R' for radians before evaluating trigonometric circular formulas.
- 💡Remember the segment area formula: Area = ½r²(θ − sin θ).
Common Mistakes
- using degree measure in the formulas s = rθ and Area = ½r²θ, which are valid only in radians
- forgetting to switch calculators to radian mode when evaluating sin θ in segment area calculations