Chapter 6 三角恒等式与方程 - 公式表

\[\sin(180° - θ) = \sin θ\] \[\cos(180° - θ) = -\cos θ\] \[\tan(180° - θ) = -\tan θ\]

\[\sin(180° + θ) = -\sin θ\] \[\cos(180° + θ) = -\cos θ\] \[\tan(180° + θ) = \tan θ\]

\[\sin(360° - θ) = -\sin θ\] \[\cos(360° - θ) = \cos θ\] \[\tan(360° - θ) = -\tan θ\]

\[\sin 30° = \frac{1}{2}, \cos 30° = \frac{\sqrt{3}}{2}, \tan 30° = \frac{1}{\sqrt{3}}\] \[\sin 45° = \frac{\sqrt{2}}{2}, \cos 45° = \frac{\sqrt{2}}{2}, \tan 45° = 1\] \[\sin 60° = \frac{\sqrt{3}}{2}, \cos 60° = \frac{1}{2}, \tan 60° = \sqrt{3}\]

\[\sin^2 θ + \cos^2 θ = 1\] \[1 + \tan^2 θ = \sec^2 θ\] \[1 + \cot^2 θ = \csc^2 θ\]

\[\sin(A ± B) = \sin A \cos B ± \cos A \sin B\] \[\cos(A ± B) = \cos A \cos B ∓ \sin A \sin B\] \[\tan(A ± B) = \frac{\tan A ± \tan B}{1 ∓ \tan A \tan B}\]

\[\sin 2θ = 2\sin θ \cos θ\] \[\cos 2θ = \cos^2 θ - \sin^2 θ = 2\cos^2 θ - 1 = 1 - 2\sin^2 θ\] \[\tan 2θ = \frac{2\tan θ}{1 - \tan^2 θ}\]

\[\sin θ = k \Rightarrow θ = \arcsin k + 2nπ \text{ 或 } θ = π - \arcsin k + 2nπ\] \[\cos θ = k \Rightarrow θ = ±\arccos k + 2nπ\] \[\tan θ = k \Rightarrow θ = \arctan k + nπ\]

\[a\sin θ + b\cos θ = c\] \[\Rightarrow \sqrt{a^2 + b^2}\sin(θ + φ) = c\] \[\text{其中 } \tan φ = \frac{b}{a}\]

\[\text{恒等式：对所有定义域内的值都成立}\] \[\text{方程：只对特定值成立}\]

\[\text{从左到右：} LHS = RHS\] \[\text{从右到左：} RHS = LHS\] \[\text{两边同时变换：} LHS = \cdots = RHS\]