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:
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.

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