### Trigonometry (Basic Formulas and Trigonometric Identity)

Trigonometry (Basic Formulas and Trigonometric Identity)

Welcome visitors..
In this post, we will explain about trigonometry.

A right triangle with hypotenuse $r$, vertical side $y$ and horizontal side $x$. Given the angle $\alpha$ formed from the sides $x$ and $r$, then there are 6 basic formulas in trigonometry, namely:
1. sin $\displaystyle \alpha =\frac{y}{r}$
2. cos $\displaystyle \alpha =\frac{x}{r}$
3. tan $\displaystyle \alpha =\frac{y}{x}$
4. csc $\displaystyle \alpha =\frac{r}{y}$
5. sec $\displaystyle \alpha =\frac{r}{x}$
6. cot $\displaystyle \alpha =\frac{x}{y}$
Description:

Trigonometry Identity
The trigonometric identity comes from the Pythagorean formula. From the triangle we have defined above, the Pythagorean formula is $x^2+y^2=r^2$. So if we divide both sides by: $x^2$ or $y^2$ or $z^2$ then we get a new formula in trigonometric form, namely:
1. $1+$tan$^2k=$sec$^2k$
2. cot$^2k+1=$csc$^2k$
3. sin$^2k+$cos$^2k=1$
Example
It is known that sin A = 1/2. Determine the value of cos A.
cos A = $\displaystyle \sqrt{1-1/4}=\frac{1}{2}\sqrt{3}$.