C09 Trigonometry
对应大纲的内容
| M5.18$ | Know and use the trigonometric ratios:
$\sin \theta = \frac{\text{opposite}}{\text{hypotenuse}}\quad$ $\cos \theta = \frac{\text{adjacent}}{\text{hypotenuse}}\quad$ $\tan \theta = \frac{\text{opposite}}{\text{adjacent}}$ Apply these to find angles and lengths in right-angled triangles and, where possible, general triangles in 2- and 3-dimensional figures. Know the exact values of $\sin \theta$ and $\cos \theta$ for $\theta = 0^\circ$, $30^\circ$, $45^\circ$, $60^\circ$, $90^\circ$. Know the exact values of $\tan \theta$ for $\theta = 0^\circ$, $30^\circ$, $45^\circ$, $60^\circ$. Candidates are not expected to recall or use the sine or cosine rules. |
学习目标
- Synthesise trigonometric definitions by transitioning fluently between right-angled triangles and Cartesian coordinates $(x, y, r)$ to evaluate angles of any magnitude.
- Determine quadrant signs and reference angles by applying the ASTC (All, Sine, Tangent, Cosine) rules to deduce the signs of trigonometric functions and reducing obtuse or reflex angles to their acute reference counterparts.
- Master radian measure by converting fluently between degrees and radians, applying them directly to calculate arc lengths $(s=r \theta)$ and circular sector areas $\left(A=\frac{1}{2} r^2 \theta\right)$. Execute exact value and identity manipulations by recalling surd values for fundamental angles ( $0$, $\frac{\pi}{6}$, $\frac{\pi}{4}$, $\frac{\pi}{3}$, $\frac{\pi}{2}$ ) and simplifying expressions using quotient, even/odd, and cofunction identities.
- Analyse trigonometric graphs by deconstructing the periodic curves of $y=\sin x$, $y=\cos x$ and $y=\tan x$ to identify their exact periods, bounded ranges, and asymptotic limits.
建议时间
| Task | No. of Questions | Suggested Time |
|---|---|---|
| Examples | 7 | 100 min |
| Quiz | 8 | 25 min |
| Practice A | 20 | 30 min |
| Practice B | 15 | 45 min |
| Total | 50 | approx. 3-4 hrs |
