Trigonometry (A2 Unit 3: Pure Mathematics B) — WJEC A-Level Mathematics
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Trigonometry (A2 Unit 3: Pure Mathematics B) explained
Exact trigonometric ratios derive from standard reference triangles: the equilateral triangle of side 2 split in half gives angles π/6 (30°) and π/3 (60°) with sides 1, √3, 2, yielding sin(π/6) = 1/2, cos(π/6) = √3/2, tan(π/6) = 1/√3; sin(π/3) = √3/2, cos(π/3) = 1/2, tan(π/3) = √3. The isosceles right-angled triangle with legs 1, 1 and hypotenuse √2 gives angle π/4 (45°), yielding sin(π/4) = 1/√2, cos(π/4) = 1/√2, tan(π/4) = 1. Boundary values from the unit circle give sin 0 = 0, cos 0 = 1, tan 0 = 0; sin(π/2) = 1, cos(π/2) = 0, tan(π/2) undefined; sin π = 0, cos π = −1, tan π = 0. Values in other quadrants are found by determining the reference angle and attaching quadrant signs from the CAST diagram.
Your focus
- State exact values of sine, cosine, and tangent for special angles 0, π/6, π/4, π/3, π/2, and π.
- Evaluate exact trigonometric ratios for any integer multiple of special angles across all quadrants.
- Derive exact values using equilateral and isosceles right-angled reference triangles.
Trigonometry (A2 Unit 3: Pure Mathematics B) exam tips
Marking Points
- stating exact values of sin, cos, and tan for π/6, π/4, and π/3 in surd form
- evaluating exact trigonometric ratios at quadrantal angles 0, π/2, π, 3π/2, and 2π
- calculating exact values for angles in quadrants 2, 3, and 4 using reference angles and the CAST diagram
Examiner Tips
- 💡Memorise the exact values or sketch the two standard reference triangles at the top of your script.
- 💡Keep answers as exact fractions with surds (e.g. √3/2, 1/√2) unless decimals are requested.
Common Mistakes
- giving decimal approximations instead of exact surd fractions when exact values are required
- confusing sin(π/6) = 1/2 with sin(π/3) = √3/2