Basic Technical Mathematics, 11th Edition

TRIGONOMETRY

$\sin \theta \hspace{0.17em}=\hspace{0.17em}\frac{{\displaystyle y}}{{\displaystyle r}}\cos \theta \hspace{0.17em}=\hspace{0.17em}\frac{{\displaystyle x}}{{\displaystyle r}}\tan \theta \hspace{0.17em}=\hspace{0.17em}\frac{{\displaystyle y}}{{\displaystyle x}}\cot \theta \hspace{0.17em}=\hspace{0.17em}\frac{{\displaystyle x}}{{\displaystyle y}}\sec \theta \hspace{0.17em}=\hspace{0.17em}\frac{{\displaystyle r}}{{\displaystyle x}}\csc \theta \hspace{0.17em}=\hspace{0.17em}\frac{{\displaystyle r}}{{\displaystyle y}}$

Law of Sines: $\frac{{\displaystyle a}}{{\displaystyle \sin A}}\hspace{0.17em}=\hspace{0.17em}\frac{{\displaystyle b}}{{\displaystyle \sin B}}\hspace{0.17em}=\hspace{0.17em}\frac{{\displaystyle c}}{{\displaystyle \sin C}}\pi \text{ rad}\hspace{0.17em}=\hspace{0.17em}180\hspace{0.17em}°\hspace{0.17em}$

Law of Cosines: $a^2\hspace{0.17em}=\hspace{0.17em}{b}^2\hspace{0.17em}+\hspace{0.17em}{c}^2\hspace{0.17em}-\hspace{0.17em}2bc\cos A$

Basic Identities

$\sin \theta \hspace{0.17em}=\hspace{0.17em}\frac{{\displaystyle 1}}{{\displaystyle \csc \theta }}\cos \theta \hspace{0.17em}=\hspace{0.17em}\frac{{\displaystyle 1}}{{\displaystyle \sec \theta }}\tan \theta \hspace{0.17em}=\hspace{0.17em}\frac{{\displaystyle 1}}{{\displaystyle \cot \theta }}\tan \theta \hspace{0.17em}=\hspace{0.17em}\frac{{\displaystyle \sin \theta }}{{\displaystyle \cos \theta }}\cot \theta \hspace{0.17em}=\hspace{0.17em}\frac{{\displaystyle \cos \theta }}{{\displaystyle \sin \theta }}$

${\sin }^2\theta \hspace{0.17em}+\hspace{0.17em}{\cos }^2\theta \hspace{0.17em}=\hspace{0.17em}11\hspace{0.17em}+\hspace{0.17em}{\tan }^2\theta \hspace{0.17em}=\hspace{0.17em}{\text{sec}}^2\theta 1\hspace{0.17em}+\hspace{0.17em}{\cot }^2\theta \hspace{0.17em}+\hspace{0.17em}{\csc }^2\theta$

$\sin 2\alpha \hspace{0.17em}=\hspace{0.17em}2\sin \alpha \cos \alpha \cos 2\alpha \hspace{0.17em}=\hspace{0.17em}{\cos }^2\alpha \hspace{0.17em}-\hspace{0.17em}{\sin }^2\alpha \hspace{0.17em}=\hspace{0.17em}2{\cos }^2\alpha \hspace{0.17em}-\hspace{0.17em}1\hspace{0.17em}=\hspace{0.17em}1\hspace{0.17em}-\hspace{0.17em}2{\sin }^2\alpha$

$\sin \frac{{\displaystyle \alpha }}{{\displaystyle 2}}\hspace{0.17em}=\hspace{0.17em}\hspace{0.17em}\pm \hspace{0.17em}\sqrt{\frac{{\displaystyle 1\hspace{0.17em}-\hspace{0.17em}\cos \alpha }}{{\displaystyle 2}}}\cos \frac{{\displaystyle \alpha }}{{\displaystyle 2}}\hspace{0.17em}=\hspace{0.17em}\hspace{0.17em}\pm \hspace{0.17em}\sqrt{\frac{{\displaystyle 1\hspace{0.17em}+\hspace{0.17em}\cos \alpha }}{{\displaystyle 2}}}$