C08 Trigonometric Identities
对应大纲的内容
| MM4.2 | Radian measure, including use for arc length and area of sector and segment. |
| MM4.3 | The values of sine, cosine and tangent for the angles: $0^\circ$, $30^\circ$, $45^\circ$, $60^\circ$, $90^\circ$. |
| MM4.4 | The sine, cosine and tangent functions; their graphs, symmetries, and periodicity. |
| MM4.5 | Knowledge and use of the equations:
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学习目标
- Master core trigonometric identities by rigorously applying $\tan \theta \equiv$ $\frac{\sin \theta}{\cos \theta}$ and $\sin ^2 \theta$ $+$ $\cos ^2 \theta$ $\equiv 1$ to simplify complex algebraic fractions, isolate variables, and prove structural equivalences.
- Deconstruct disguised quadratics by using the Pythagorean identity to transform mixed-base trigonometric equations into standard quadratic polynomials, allowing for the systematic solution of single ratios.
- Synthesise graphical symmetries and periodicity by mapping the periodic intervals, reflectional and rotational symmetries, and asymptotic limits of $y=\sin x$, $y=\cos x$, and $y=\tan x$ to deduce secondary roots.
建议时间
| Task | No. of Questions | Suggested Time |
|---|---|---|
| Examples | 8 | 120 min |
| Quiz | 5 | 20 min |
| Practice A | 20 | 40 min |
| Practice B | 20 | 50 min |
| Total | 53 | approx. 3-4 hrs |
Practice:
