OCR MEI AS Paper 2 Specimen — Question 12 3 marks

Exam BoardOCR MEI
ModuleAS Paper 2 (AS Paper 2)
SessionSpecimen
Marks3
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Mark schemeDownload PDF ↗
TopicTrig Proofs
TypeProve using Pythagorean identity result
DifficultyStandard +0.3 This is a straightforward proof following a given hint. Students let θ = arcsin x, immediately get sin θ = x and cos θ = y from the given equation, then apply sin²θ + cos²θ = 1 to reach x² + y² = 1. It requires only direct application of definitions and the Pythagorean identity with minimal problem-solving, making it slightly easier than average.
Spec1.05i Inverse trig functions: arcsin, arccos, arctan domains and graphs1.05j Trigonometric identities: tan=sin/cos and sin^2+cos^2=1
12 Given that \(\arcsin x = \arccos y\), prove that \(x ^ { 2 } + y ^ { 2 } = 1\). [Hint: Let \(\arcsin x = \theta\) ] \section*{END OF QUESTION PAPER}
Question 12:
AnswerMarks Guidance
\(\arcsin x = \theta \Rightarrow x = \sin\theta\)M1 AO1.1
\(\arccos y = \theta \Rightarrow y = \cos\theta\)M1 AO1.1
\(\sin^2\theta + \cos^2\theta = 1\)
AnswerMarks Guidance
\(\Rightarrow x^2 + y^2 = 1\) AGE1 [3] AO2.1 
## Question 12:

$\arcsin x = \theta \Rightarrow x = \sin\theta$ | M1 | AO1.1

$\arccos y = \theta \Rightarrow y = \cos\theta$ | M1 | AO1.1

$\sin^2\theta + \cos^2\theta = 1$

$\Rightarrow x^2 + y^2 = 1$ AG | E1 [3] | AO2.1
12 Given that $\arcsin x = \arccos y$, prove that $x ^ { 2 } + y ^ { 2 } = 1$. [Hint: Let $\arcsin x = \theta$ ]

\section*{END OF QUESTION PAPER}

\hfill \mbox{\textit{OCR MEI AS Paper 2  Q12 [3]}}
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