Question 2 - A-Level Maths

Exam Board	OCR MEI
Module	C3 (Core Mathematics 3)
Year	2005
Session	June
Marks	3
Paper	Download PDF ↗
Mark scheme	Download PDF ↗
Topic	Reciprocal Trig & Identities
Type	Inverse trigonometric function equations
Difficulty	Easy -1.2 This is a straightforward question requiring only direct evaluation of arcsin at a standard angle (π/6) and recall of the complementary relationship arcsin x + arccos x = π/2. No problem-solving or multi-step reasoning required—purely routine application of inverse trig definitions and a basic identity.
Spec	1.05i Inverse trig functions: arcsin, arccos, arctan domains and graphs

2 Given that \(\arcsin x = \frac { 1 } { 6 } \pi\), find \(x\). Find \(\arccos x\) in terms of \(\pi\).

Answer	Marks	Guidance
\(x = 1/2\) and \(\cos \theta = 1/2 \Rightarrow \theta = \pi/3\)	B1, M1, A1 [3]	M1A0 for 1.04... or 60°

$x = 1/2$ and $\cos \theta = 1/2 \Rightarrow \theta = \pi/3$ | B1, M1, A1 [3] | M1A0 for 1.04... or 60°

2 Given that $\arcsin x = \frac { 1 } { 6 } \pi$, find $x$. Find $\arccos x$ in terms of $\pi$.

\hfill \mbox{\textit{OCR MEI C3 2005 Q2 [3]}}