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Trigonometry and Identities

Quick questions on Trigonometric ratios and the unit circle explained: O-Level A-Maths

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 the unit-circle definitions?
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Take a point PP on the circle of radius 11 centred at the origin, where the radius to PP makes an angle θ\theta measured anticlockwise from the positive xx-axis. Then:
What is signs by quadrant?
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As PP moves round, the signs of xx and yy change, so the ratios change sign. The pattern (often remembered as "All, Sine, Tangent, Cosine") is:
What are reference angles?
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The reference angle is the acute angle between the radius and the horizontal axis. The size of a ratio equals the ratio of its reference angle; the quadrant fixes the sign. So sin⁡150∘=+sin⁡30∘\sin 150^\circ = +\sin 30^\circ and cos⁡210∘=−cos⁡30∘\cos 210^\circ = -\cos 30^\circ.
What is q1?
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State the sign of sin⁡200∘\sin 200^\circ and cos⁡200∘\cos 200^\circ. [2 marks]
What is q2?
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Find the exact value of sin⁡135∘\sin 135^\circ. [2 marks]
What is q3?
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Given cos⁡θ=513\cos\theta = \dfrac{5}{13} with θ\theta acute, find sin⁡θ\sin\theta. [2 marks]

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