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6 marksTrigonometric Functions, Identities and Equations

CAPE Pure Mathematics Unit 1 · May/June 2003 · Paper 2 · Question 1(c)(i)

A wedge in an electrical appliance is in the form of a sector of a circle, with centre O and radius 4 cm. Angle AOB measures π/4 radians. The diagram is not drawn to scale.

Show that the area of the shaded region is 2(π - 2√2).

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Other parts of this question

  1. 1(a)Find p and q. Hence, find the remainder when x² + px + q is divided by (x + 1).[7 marks]
  2. 1(b)(i)Calculate to 3 significant figures the length of BC.[4 marks]
  3. 1(b)(ii)Calculate to 3 significant figures the value of sin C.[4 marks]
  4. 1(c)(ii)Using the cosine rule, show that the length of the chord AB is 4√(2 - √2).[4 marks]

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