OCR MEI C3 — Question 3 3 marks

Exam BoardOCR MEI
ModuleC3 (Core Mathematics 3)
Marks3
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicReciprocal Trig & Identities
TypeInverse trigonometric function equations
DifficultyStandard +0.3 This is a straightforward proof following a given hint. Students let θ = arcsin x, write x = sin θ and y = cos θ (since arcsin x = arccos y = θ), then apply the Pythagorean identity sin²θ + cos²θ = 1. It requires understanding inverse trig functions and applying a standard identity, but the hint makes it a guided exercise rather than requiring independent insight.
Spec1.01a Proof: structure of mathematical proof and logical steps1.05i Inverse trig functions: arcsin, arccos, arctan domains and graphs
3 Given that \(\arcsin x = \arccos y\), prove that \(x ^ { 2 } + y ^ { 2 } = 1\). [Hint: let \(\arcsin x = \theta\).]
Question 3:
AnswerMarks
Let \(\arcsin x = \theta \Rightarrow x = \sin\theta\)M1
\(\theta = \arccos y \Rightarrow y = \cos\theta\)M1
\(\sin^2\theta + \cos^2\theta = 1 \Rightarrow x^2 + y^2 = 1\)E1 [3] 
## Question 3:

| Let $\arcsin x = \theta \Rightarrow x = \sin\theta$ | M1 | |
|---|---|---|
| $\theta = \arccos y \Rightarrow y = \cos\theta$ | M1 | |
| $\sin^2\theta + \cos^2\theta = 1 \Rightarrow x^2 + y^2 = 1$ | E1 [3] | |

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

\hfill \mbox{\textit{OCR MEI C3  Q3 [3]}}
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