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NSWMaths AdvancedQuick questions
Year 11: Exponential and Logarithmic Functions
Quick questions on Radian measure, arcs and sectors for HSC Maths Advanced: the definition of a radian as arc length over radius, converting between degrees and radians with pi rad = 180 deg, the exact radian values of common angles, the arc-length formula L = r theta, the sector-area formula A = half r squared theta, and the area of a segment as a sector minus a triangle, with code-checked numbers and diagrams
4short 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 exact radian values worth memorising?Show answer
A handful of angles come up constantly, so learn their radian forms by sight rather than converting each time. They are just times the degree value, cancelled:
What is arc length?Show answer
The arc-length formula falls straight out of the definition. Since , multiplying both sides by gives
What is sector area?Show answer
A sector is the "pizza slice" region bounded by the two radii and the arc. Its area is the fraction of the whole circle (the angle as a share of a full turn), and the whole circle has area :
What is segment area?Show answer
A chord joins the two ends of an arc and slices off a segment, the region between the chord and the arc. To find its area, draw the two radii to the ends of the chord. They split the figure into the sector and the isosceles triangle , and the minor segment is what is left when the triangle is taken out of the sector:
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