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NSWMaths AdvancedQuick questions

Year 12: Trigonometric Functions

Quick questions on Radians, arc length, sector and segment area for HSC Maths Advanced

5short 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 arc length?
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For a sector of radius rr with central angle θ\theta in radians, the arc length is
What is sector area?
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The area of a sector of radius rr with central angle θ\theta in radians is
What is chord length?
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By the cosine rule (or by splitting the isosceles triangle), the chord opposite the central angle θ\theta has length
What is wrong formula for the triangle?
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The triangle area is 12r2sin⁡θ\frac{1}{2} r^2 \sin \theta (with sin⁡θ\sin \theta, not θ\theta). Confusing this with the sector formula gives a wrong segment.
What is calculator in the wrong mode?
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Always check that your calculator is in radian mode when working from π6\frac{\pi}{6} etc.

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