Trigonometry Advanced Quiz 1

$\frac{a}{\mathrm{sinA}}=\frac{b}{\mathrm{sinB}}=\frac{c}{\mathrm{sinC}}$ $a^2=b^2+c^2-2bccosA$ $\mathrm{sinA}+\mathrm{sinB}+\mathrm{sinC}=180°$

$a^2=b^2+c^2-2bccosA$ $\frac{a}{\mathrm{sinA}}=\frac{b}{\mathrm{sinB}}=\frac{c}{\mathrm{sinC}}$ $a=b+c$

$\sin \left(2x\right)=2\sin \left(x\right)\cos \left(x\right)$ $\sin \left(2x\right)={\sin }^2\left(x\right)-{\cos }^2\left(x\right)$ $\sin \left(2x\right)=\frac{2\tan \left(x\right)}{1+{\tan }^2\left(x\right)}$

$\cos \left(2x\right)={\cos }^2\left(x\right)-{\sin }^2\left(x\right)$ $\cos \left(2x\right)=2\sin \left(x\right)\cos \left(x\right)$ $\cos \left(2x\right)=1-2{\sin }^2\left(x\right)$

$\sin (A+B)=\sin A\cos B+\cos A\sin B$ $\sin (A+B)=\sin A\sin B+\cos A\cos B$ $\sin (A+B)=\sin A+\sin B$

$\cos (A+B)=\cos A\cos B-\sin A\sin B$ $\cos (A+B)=\cos A\sin B+\sin A\cos B$ $\cos (A+B)=\cos A+\cos B$

$1+{\tan }^2\left(x\right)={\sec }^2\left(x\right)$ $1+{\cot }^2\left(x\right)={\csc }^2\left(x\right)$ ${\tan }^2\left(x\right)+{\sec }^2\left(x\right)=1$

$1+{\cot }^2\left(x\right)={\csc }^2\left(x\right)$ $1+{\tan }^2\left(x\right)={\sec }^2\left(x\right)$ ${\cot }^2\left(x\right)+{\csc }^2\left(x\right)=1$

Arcsin Arccos Arctan

Arctan Arcsin Arccos