OCR MEI C3 2010 January — Question 7 3 marks

Exam BoardOCR MEI
ModuleC3 (Core Mathematics 3)
Year2010
SessionJanuary
Marks3
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicReciprocal Trig & Identities
TypeInverse trigonometric function equations
DifficultyStandard +0.3 This is a straightforward proof using the hint provided. Students let θ = arcsin x, so x = sin θ and y = cos θ (from the given equation), then apply the Pythagorean identity sin²θ + cos²θ = 1. The hint makes it direct, requiring only basic understanding of inverse trig functions and a standard identity, making it slightly easier than average.
Spec1.01a Proof: structure of mathematical proof and logical steps1.05i Inverse trig functions: arcsin, arccos, arctan domains and graphs
7 Given that \(\arcsin x = \arccos y\), prove that \(x ^ { 2 } + y ^ { 2 } = 1\). [Hint: let \(\arcsin x = \theta\).] Section B (36 marks)
Question 7:
AnswerMarks Guidance
AnswerMarks Guidance
Let \(\arcsin x = \theta \Rightarrow x = \sin\theta\)M1
\(\theta = \arccos y \Rightarrow y = \cos\theta\)M1
\(\sin^2\theta + \cos^2\theta = 1\)E1
\(\Rightarrow x^2 + y^2 = 1\)[3] 
# Question 7:
| Answer | Marks | Guidance |
|--------|-------|----------|
| Let $\arcsin x = \theta \Rightarrow x = \sin\theta$ | M1 | |
| $\theta = \arccos y \Rightarrow y = \cos\theta$ | M1 | |
| $\sin^2\theta + \cos^2\theta = 1$ | E1 | |
| $\Rightarrow x^2 + y^2 = 1$ | [3] | |

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7 Given that $\arcsin x = \arccos y$, prove that $x ^ { 2 } + y ^ { 2 } = 1$. [Hint: let $\arcsin x = \theta$.]

Section B (36 marks)\\

\hfill \mbox{\textit{OCR MEI C3 2010 Q7 [3]}}
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Q1 4 Q2 6 Q3 7 Q4 8 Q5 4 Q6 4 Q7 3 Q8 17 Q9 19