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Core Pure: polar coordinates and hyperbolic functions

Quick questions on Area in polar coordinates: one half integral r squared d theta, loops and areas between curves - OCR A-Level Further Maths A

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 are wrong loop limits?
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A single loop runs between consecutive zeros of rr; using 00 to 2π2\pi for a multi-loop curve counts several loops (or cancels overlaps) and gives a wrong area.
What is not linearising the square?
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sin⁡2θ\sin^2\theta and cos⁡2θ\cos^2\theta must be rewritten with double-angle identities before integrating; integrating them directly is not valid.
What is q1?
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Write the integral for the area enclosed by r=1+cos⁡θr = 1 + \cos\theta for 0≤θ≤2π0 \le \theta \le 2\pi. [2 marks]
What is q2?
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State the double-angle identity you would use to integrate cos⁡2θ\cos^2\theta. [1 mark]

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