| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9794/1 (Pre-U Mathematics Paper 1) |
| Year | 2014 |
| Session | June |
| Marks | 3 |
| Topic | Trig Graphs & Exact Values |
| Type | Sketch trig curve and its inverse and state geometric relationship |
| Difficulty | Moderate -0.8 This question requires sketching two standard curves (tan x and arctan x) and recognizing they are reflections in y=x. While it involves understanding inverse functions geometrically, the sketches are routine and the relationship is a standard fact about inverse functions requiring minimal problem-solving. |
| Spec | 1.02m Graphs of functions: difference between plotting and sketching1.05a Sine, cosine, tangent: definitions for all arguments1.05i Inverse trig functions: arcsin, arccos, arctan domains and graphs |
Correct and labelled tan curve with asymptotes clearly intended or shown. Scale required on $x$-axis — B1
Correct arc tan curve — B1
$\tan^{-1}\left(\frac{\pi}{2}\right)$ must be approx. 1 or asymptote shown. Scale required on $y$-axis
State reflection in line $y = x$ — B1 **[3]**2 Sketch the curve with equation $y = \tan x$ for $- \frac { 1 } { 2 } \pi < x < \frac { 1 } { 2 } \pi$.\\
On the same diagram, sketch the curve with equation $y = \tan ^ { - 1 } x$ for all $x$.\\
State the geometrical relationship between the curves.
\hfill \mbox{\textit{Pre-U Pre-U 9794/1 2014 Q2 [3]}}