$$\cos^2\theta+\sin^2\theta=1$$ $$1+\tan^2\theta=\sec^2\theta$$ $$1+\cot^2\theta=\csc^2\theta$$ $$\sin^2\theta=1-\cos^2\theta=\frac{1-\cos2\theta}{2}$$ $$\cos^2\theta=1-\sin^2\theta=\frac{1+\cos2\theta}{2}$$

$$\cos(A\pm B)=\cos A\cos B\mp\sin A\sin B$$ $$\sin(A\pm B)=\sin A\cos B\pm\cos A\sin B$$ $$\tan(A\pm B)=\frac{\tan A\pm\tan B}{1\mp\tan A\tan B}$$

$$\cos2A=\cos^2A-\sin^2A=2\cos^2A-1=1-2\sin^2A$$ $$\sin2A=2\sin A\cos A$$ $$\tan2A=\frac{2\tan A}{1-\tan^2A}$$

$$\cos\tfrac{A}{2}=\pm\sqrt{\frac{1+\cos A}{2}}$$ $$\sin\tfrac{A}{2}=\pm\sqrt{\frac{1-\cos A}{2}}$$ $$\tan\tfrac{A}{2}=\pm\sqrt{\frac{1-\cos A}{1+\cos A}}=\frac{1-\cos A}{\sin A}=\frac{\sin A}{1+\cos A}$$

$$\cos(\tfrac{\pi}{2}-A)=\sin A$$ $$\sin(\tfrac{\pi}{2}-A)=\cos A$$ $$\tan(\tfrac{\pi}{2}-A)=\cot A$$ $$\cot(\tfrac{\pi}{2}-A)=\tan A$$ $$\sec(\tfrac{\pi}{2}-A)=\csc A$$ $$\csc(\tfrac{\pi}{2}-A)=\sec A$$

$$\cos(-\theta)=\cos(\theta)$$ $$\sin(-\theta)=-1\cdot\sin(\theta)$$ $$\tan(-\theta)=-1\cdot\tan(\theta)$$ $$\cot(-\theta)=-1\cdot\cot(\theta)$$ $$\csc(-\theta)=-1\cdot\csc(\theta)$$ $$\sec(-\theta)=\sec(\theta)$$

$$A=\displaystyle \lim_{ n\to \infty}\sum_{i=1}^{n}f(x_{i})\Delta x$$ $$where: \Delta x=\frac{b-a}{n}$$

$$\sum_{i=1}^{n}1=n$$ $$\sum_{i=1}^{n}i=\frac{n(n+1)}{2}$$ $$\sum_{i=1}^{n}i^2=\frac{n(n+1)(2n+1)}{6}$$ $$\sum_{i=1}^{n}i^3=\left [ \frac{n(n+1)}{2} \right ]^2$$

$$\frac{\mathrm{d} }{\mathrm{d} x}\sin x=\cos x$$ $$\frac{\mathrm{d} }{\mathrm{d} x}\cos x=-\sin x$$ $$\frac{\mathrm{d} }{\mathrm{d} x}\tan x=\sec^2x$$ $$\frac{\mathrm{d} }{\mathrm{d} x}\csc x=-\csc x\cot x$$ $$\frac{\mathrm{d} }{\mathrm{d} x}\sec x=\sec x\tan x$$ $$\frac{\mathrm{d} }{\mathrm{d} x}\cot x=-\csc^2x$$

$$\frac{\mathrm{d} }{\mathrm{d} x}\sin^{-1}x=\frac{1}{\sqrt{1-x^2}}$$ $$\frac{\mathrm{d} }{\mathrm{d} x}\cos^{-1}x=-\frac{1}{\sqrt{1-x^2}}$$ $$\frac{\mathrm{d} }{\mathrm{d} x}\tan^{-1}x=\frac{1}{{1+x^2}}$$ $$\frac{\mathrm{d} }{\mathrm{d} x}\cot^{-1}x=-\frac{1}{{1+x^2}}$$ $$\frac{\mathrm{d} }{\mathrm{d} x}\sec^{-1}x=\frac{1}{x\sqrt{x^2-1}}$$ $$\frac{\mathrm{d} }{\mathrm{d} x}\csc^{-1}x=-\frac{1}{x\sqrt{x^2-1}}$$

$$\int_{}^{}udv=uv-\int_{}^{}vdu$$

$$\vec{A}=\vec{A}_xi+\vec{A}_yj+\vec{A}_zk$$ $$A^2=\mathrm{A}_{x}^{2}+\mathrm{A}_{y}^{2}+\mathrm{A}_{z}^{2}$$ $$\vec{A}\cdot \vec{B}=AB\cos\theta$$ $$\vec{A}\cdot \vec{B}=A_xB_x+A_yB_y+A_zB_z$$ $$\left|\vec{A}\times\vec{B}\right|=AB\sin\theta$$ $$\vec{A}\times\vec{B}=(A_yB_z-B_yA_z)i+(A_zB_x-B_zA_x)j+(A_xB_y-B_xA_y)k$$

$$\vec{r}=\vec{r}_0+\vec{v}_0t+\tfrac{1}{2}\vec{a}t^2$$ $$\Delta x=\tfrac{1}{2}(v_0+v)t$$ $$\vec{v}=\vec{v}_0+\vec{a}t$$ $$v_x^2=v_{x0}^2+2a_x(x-x_0)$$ $$\vec{v}=\frac{d\vec{r}}{dt}$$ $$\vec{a}=\frac{d\vec{v}}{dt}$$

$$\Sigma\vec{F}=m\vec{a}$$ $$F_g=mg$$ $$F_{sp}=-kx$$

$$W=F_x\Delta x$$ $$W=\vec{F}\cdot\Delta\vec{r}$$ $$W=\int_{\vec{r_1}}^{\vec{r_2}}\vec{F}\cdot d\vec{r}$$ $$P=\frac{dW}{dt}=\vec{F}\cdot\vec{v}$$ $$P=\frac{dE}{dt}$$ $$W_{net}=\Delta K$$ $$W_{nc}=\Delta E$$

$$K=\tfrac{1}{2}mv^2$$ $$W_{net}=\Delta K$$ $$W_{nc}=\Delta E$$ $$\Delta U=-\int_{A}^{B}\vec{F}\cdot d\vec{r}$$ $$\Delta U_g=mgh$$ $$U_{sp}=\tfrac{1}{2}kx^2$$