Some A level students were given the following question - Edexcel - A-Level Maths Pure - Question 2 - 2017 - Paper 1
Question 2
Some A level students were given the following question.
Solve, for $-90^{\circ} < \theta < 90^{\circ}$, the equation
$$cos \theta = 2 sin \theta$$
The attempts o... show full transcript
Worked Solution & Example Answer:Some A level students were given the following question - Edexcel - A-Level Maths Pure - Question 2 - 2017 - Paper 1
Step 1
Identify an error made by student A.
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Answer
Student A incorrectly uses the relation sinθcosθ=tanθ. The correct relation should be ( \frac{sin \theta}{cos \theta} = tan \theta ), leading to the realization that they incorrectly derived the equation.
Step 2
Explain why $\theta = -26.6^{\circ}$ is not a solution of $cos \theta = 2 sin \theta$.
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Answer
To verify, substitute θ=−26.6∘ into the equation:
cos(−26.6∘)=2sin(−26.6∘).
Calculating both sides:
Left side: cos(−26.6∘)=cos(26.6∘) (due to the even property of cosine).
Right side: 2sin(−26.6∘)=−2sin(26.6∘) (since sine is odd).
Thus, cos(26.6∘)=−2sin(26.6∘), confirming it is not a solution.
Step 3
Explain how this incorrect answer arose.
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Answer
The incorrect answer θ=−26.6∘ likely arose from squaring both sides of the equation prematurely, which can introduce extraneous solutions. By squaring, one loses the distinction between positive and negative roots, which can yield answers that do not satisfy the original equation.
