Q281 · Practice questionTechnology-freeSimple familiar5 marks
QUESTION 281 (5 marks)
A calibration calculation requires
a)[2 marks]
Rewrite both squared trigonometric terms using suitable identities.
b)[3 marks]
Determine I exactly.
WORKED SOLUTION
5 marksPractice marking scheme
ANSWER
(a) , . (b) .
Worked solution
(a) Use the Pythagorean and double-angle identities. The combined integrand is .
(b) Integrate to obtain . The sine term vanishes at both endpoints, so .
Equivalent justified methods accepted; respect any requested proof method.
Exact values unless specified. Sketches assessed by mathematical features, not artistic quality.
Part a: Use the secant-tangent identity.
Part a: Use the correct double-angle identity with argument 2x.
Part b: Integrate the secant term correctly.
Part b: Integrate the constant and cosine terms with correct factors.
Part b: Apply both bounds and simplify.
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