Rumus fungsi trigonometri

Rumus-rumus untuk bekerja dengan fungsi trigonometri.

Rumus asas

$$\begin{array}{rcl}{\sin }^2(x)+{\mathrm{kos}}^2(x)& =& 1\\ \tan (x)\cdot \mathrm{kot}(x)& =& 1\\ \sin (x)& =& \mathrm{kos}(x-\frac{\pi }{2})\\ \mathrm{kos}(x)& =& \sin (x+\frac{\pi }{2})\\ \mathrm{kot}(x)& =& \tan (-x+\frac{\pi }{2})\end{array}$$

Tangen dan kotangen dalam sebutan sinus dan kosinus

$$\begin{array}{rcl}\tan (x)& =& \frac{\sin (x)}{\mathrm{kos}(x)}\\ \mathrm{kot}(x)& =& \frac{\mathrm{kos}(x)}{\sin (x)}\end{array}$$

Rumus sudut berganda dan sudut separuh (2x dan x/2)

$$\begin{array}{rcl}\sin (2x)& =& 2\sin (x)\mathrm{kos}(x)\\ \mathrm{kos}(2x)& =& {\mathrm{kos}}^2(x)-{\sin }^2(x)\\ |\sin (\frac{x}{2})|& =& \sqrt{\frac{1-\mathrm{kos}(x)}{2}}\\ |\mathrm{kos}(\frac{x}{2})|& =& \sqrt{\frac{1+\mathrm{kos}(x)}{2}}\end{array}$$

Rumus sudut majmuk

$$\begin{array}{rcl}\sin (x+y)& =& \sin (x)\mathrm{kos}(y)+\mathrm{kos}(x)\sin (y)\\ \sin (x-y)& =& \sin (x)\mathrm{kos}(y)-\mathrm{kos}(x)\sin (y)\\ \mathrm{kos}(x+y)& =& \mathrm{kos}(x)\mathrm{kos}(y)-\sin (x)\sin (y)\\ \mathrm{kos}(x-y)& =& \mathrm{kos}(x)\mathrm{kos}(y)+\sin (x)\sin (y)\end{array}$$