62 Formule de trigonometrie disponibile

$\sin^2 x + \cos^2 x = 1$

$\sin(\frac{\pi}{2} - x) = \cos x$

$\sin 2x = 2 \sin x \cos x$

$\cos 2x = \cos^2 x - \sin^2 x = 2\cos^2 x - 1 = 1 - 2\sin^2 x$

$\tg 2x = \frac{2 \tg x}{1 - \tg^2 x}$

$\sin^2 x = \frac{1 - \cos 2x}{2}$

$\cos^2 x = \frac{1 + \cos 2x}{2}$

$\sin 3x = 4\sin^3 x - 3\sin x$

$\cos 3x = 4\cos^3 x - 3\cos x$

$\sin(a + b) = \sin a \cos b + \cos a \sin b$

$\cos(a + b) = \cos a \cos b - \sin a \sin b$

$\sin(a - b) = \sin a \cos b - \cos a \sin b$

$\cos(a - b) = \cos a \cos b + \sin a \sin b$

$\tg(a \pm b) = \frac{\tg a \pm \tg b}{1 \mp \tg a \cdot \tg b}$

$\tg \frac{a}{2} = \frac{1 - \cos a}{\sin a}$

$\left|\cos \frac{a}{2}\right| = \sqrt{\frac{1 + \cos a}{2}}$

$\left|\sin \frac{a}{2}\right| = \sqrt{\frac{1 - \cos a}{2}}$

$\sin a \cdot \cos b = \frac{1}{2}[\sin(a+b) + \sin(a-b)]$

$\cos a \cdot \cos b = \frac{1}{2}[\cos(a+b) + \cos(a-b)]$

$\sin a \cdot \sin b = -\frac{1}{2}[\cos(a+b) - \cos(a-b)]$

$\cos a + \cos b = 2\cos \frac{a+b}{2} \cos \frac{a-b}{2}$

$\cos a - \cos b = -2\sin \frac{a+b}{2} \sin \frac{a-b}{2}$

$\sin a + \sin b = 2\sin \frac{a+b}{2} \cos \frac{a-b}{2}$

$\sin a - \sin b = 2\sin \frac{a-b}{2} \cos \frac{a+b}{2}$

$\tg a + \tg b = \frac{\sin(a+b)}{\cos a \cos b}$

$\tg a - \tg b = \frac{\sin(a-b)}{\cos a \cos b}$

$\sin a = \frac{2\tg \frac{a}{2}}{1 + \tg^2 \frac{a}{2}}$

$\cos a = \frac{1 - \tg^2 \frac{a}{2}}{1 + \tg^2 \frac{a}{2}}$

$\tg a = \frac{2\tg \frac{a}{2}}{1 - \tg^2 \frac{a}{2}}$

$z = r(\cos \varphi + i \sin \varphi)$

$z_1 \cdot z_2 = r_1r_2[\cos (\varphi_1 + \varphi_2) + i \sin (\varphi_1 + \varphi_2)]$

$z_1^n = r_1^n(\cos n\varphi_1 + i \sin n\varphi_1)$

$\lim_{x \to 0} \frac{\sin x}{x} = 1$

$\lim_{x \to 0} \frac{\tg x}{x} = 1$

$(\sin u)' = \cos u \cdot u'$

$(\cos u)' = -\sin u \cdot u'$

$(\tg u)' = \frac{1}{\cos^2 u} \cdot u'$

$(\ctg u)' = -\frac{1}{\sin^2 u} \cdot u'$

$(\arcsin u)' = \frac{1}{\sqrt{1-u^2}} \cdot u'$

$(\arccos u)' = -\frac{1}{\sqrt{1-u^2}} \cdot u'$

$(\arctg u)' = \frac{1}{1+u^2} \cdot u'$

$(\arcctg u)' = -\frac{1}{1+u^2} \cdot u'$

$(\sh u)' = \ch u \cdot u'$

$(\ch u)' = \sh u \cdot u'$

$\sqrt{3} \approx 1,73205$

$\vec{u} \cdot \vec{v} = x_ux_v + y_uy_v$

$\vec{u} \cdot \vec{v} = |\vec{u}| |\vec{v}| \cos(\sphericalangle(\vec{u},\vec{v}))$

$a^2 = b^2 + c^2 - 2bc \cos A$

$\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C} = 2R$

$\sin \frac{A}{2} = \sqrt{\frac{(p-b)(p-c)}{bc}}$

$\cos \frac{A}{2} = \sqrt{\frac{p(p-a)}{bc}}$

$\begin{array}{|c|c|c|c|c|c|}\hline x & 0^\circ & 30^\circ & 45^\circ & 60^\circ & 90^\circ \\\hline\sin x & 0 & \frac{1}{2} & \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{2} & 1 \\\hline\end{array}$

$\begin{array}{|c|c|c|c|c|c|}\hline x & 0^\circ & 30^\circ & 45^\circ & 60^\circ & 90^\circ \\\hline\cos x & 1 & \frac{\sqrt{3}}{2} & \frac{\sqrt{2}}{2} & \frac{1}{2} & 0 \\\hline\end{array}$

$\begin{array}{|c|c|c|c|c|c|}\hline x & 0^\circ & 30^\circ & 45^\circ & 60^\circ & 90^\circ \\\hline\tg x & 0 & \frac{\sqrt{3}}{3} & 1 & \sqrt{3} & \text{nedefinit} \\\hline\end{array}$

$\sin \left(\frac{\pi}{2} - x\right) = \cos x, \quad \forall x \in \mathbb{R}$

$\cos \left(\frac{\pi}{2} - x\right) = \sin x, \quad \forall x \in \mathbb{R}$

$\sin(-x) = -\sin x, \quad \forall x \in \mathbb{R}$

$\cos(-x) = \cos x, \quad \forall x \in \mathbb{R}$

$\sin(x + 2k\pi) = \sin x, \quad \forall k \in \mathbb{Z}$

$\cos(x + 2k\pi) = \cos x, \quad \forall k \in \mathbb{Z}$

$\tg(x + k\pi) = \tg x, \quad \forall k \in \mathbb{Z}$

$\ctg(x + k\pi) = \ctg x, \quad \forall k \in \mathbb{Z}$