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SingaporeAdditional MathematicsQuick questions

Trigonometry and Identities

Quick questions on Trigonometric ratios and the unit circle: N(A)-Level Additional Mathematics

8short 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 is the unit-circle definition?
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Draw a circle of radius 11 centred at the origin. For an angle θ\theta measured anticlockwise from the positive xx-axis, the point where the radius meets the circle has coordinates (cos⁡θ, sin⁡θ)(\cos\theta,\ \sin\theta). So:
What are signs in the four quadrants?
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The signs of xx and yy change from quadrant to quadrant, so the ratios do too. The memory aid is "All, Sine, Tangent, Cosine" (sometimes "All Students Take Cake"), read anticlockwise from the first quadrant:
What are exact values of standard angles?
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These come from the 4545-4545-9090 and 3030-6060-9090 triangles and should be memorised:
What is using a related acute angle?
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For an angle outside the first quadrant, find the acute angle it makes with the xx-axis (the basic or reference angle), evaluate the ratio for that acute angle, then attach the sign from the correct quadrant. For example cos⁡150∘=−cos⁡30∘=−32\cos 150^\circ = -\cos 30^\circ = -\tfrac{\sqrt{3}}{2}.
What are wrong quadrant signs?
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Use the "All, Sine, Tangent, Cosine" order carefully; only one ratio (besides "all" in quadrant 1) is positive in each later quadrant.
What is q1?
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State the quadrant of 120∘120^\circ and the sign of cos⁡120∘\cos 120^\circ. [2 marks]
What is q2?
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Write down the exact value of tan⁡45∘\tan 45^\circ. [1 mark]
What is q3?
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Find the exact value of cos⁡300∘\cos 300^\circ. [2 marks]

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