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Pure mathematics: advanced

Quick questions on Trigonometry: the sine and cosine rules, graphs and exact values - OCR A-Level Maths A

6short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.

What are exact values?
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You must know the exact ratios for 0∘0^\circ, 30∘30^\circ, 45∘45^\circ, 60∘60^\circ and 90∘90^\circ without a calculator. They come from the half-equilateral triangle and the unit square.
What is the sine rule?
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The sine rule links each side of a triangle with the angle opposite it. Use it when you know two angles and any side, or two sides and a non-included angle.
What is the cosine rule?
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The cosine rule is the right tool when you know two sides and the included angle (to find the third side), or all three sides (to find an angle).
What is area of a triangle?
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When you know two sides and the angle between them, the area is 12absin⁡C\tfrac{1}{2}ab\sin C, where CC is the included angle. This is faster and more accurate than finding a perpendicular height.
What is q1?
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A triangle has sides 44 cm and 55 cm with an included angle of 60∘60^\circ. Find its area. [2 marks]
What is q2?
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In triangle ABCABC, a=8a = 8, b=11b = 11 and c=7c = 7. Find angle AA. [3 marks]

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