Trigonometry (AS Unit 1: Pure Mathematics A) — WJEC A-Level Mathematics
Test yourself on Trigonometry (AS Unit 1: Pure Mathematics A) with WJEC A-Level practice questions.
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Trigonometry (AS Unit 1: Pure Mathematics A) explained
For a general triangle ABC with side lengths a, b, c opposite angles A, B, C, standard non-right-angled formulas apply.
Read the full explanation
The sine rule states a/sin A = b/sin B = c/sin C, used when given two angles and one side, or two sides and a non-included angle (where the ambiguous case may yield two valid angle solutions since sin θ = sin(180° − θ)). The cosine rule states a² = b² + c² − 2bc cos A, used to find a third side given two sides and the included angle, or rearranged to cos A = (b² + c² − a²) / (2bc) to find an angle given all three sides. The area of the triangle is Area = ½ab sin C, which requires two sides and the sine of their included angle. These formulas require consistent pairing of opposite sides and angles.
Your focus
- Apply the sine rule to find unknown lengths and angles in non-right-angled triangles.
- Apply the cosine rule to calculate side lengths and interior angles.
- Calculate the area of general triangles using Area = ½ab sin C.
Trigonometry (AS Unit 1: Pure Mathematics A) exam tips
Marking Points
- selecting and stating the correct trigonometric rule for the given triangle data
- substituting values correctly into the sine rule, cosine rule, or area formula
- evaluating the ambiguous case of the sine rule when two angles are possible
- calculating the final side length or angle accurately with appropriate units
Examiner Tips
- 💡Check whether an angle found via the sine rule could be obtuse by checking if 180° − θ fits in the triangle.
- 💡Store full calculator values to avoid premature rounding errors in multi-step triangle questions.
Common Mistakes
- using the cosine rule with an angle that is not enclosed between the two known sides
- omitting the factor of 1/2 in the triangle area formula Area = ½ab sin C
- overlooking the obtuse angle solution in the ambiguous case of the sine rule