### 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:

sin be read "sine"

cos be read "cosine"

tan be read "tangent"

csc be read "cosecant"

sec be read "secant"

cot be read "cotangent"

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:

sin be read "sine"

cos be read "cosine"

tan be read "tangent"

csc be read "cosecant"

sec be read "secant"

cot be read "cotangent"

**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.

Answer:

From the 3rd trigonometric identity formula, we get:

cos A = $\displaystyle \sqrt{1-1/4}=\frac{1}{2}\sqrt{3}$.

Thanks for view, see you and happy learning.