# Trigonometric functions

In the right triangle is:

$\text{ tg} \ \alpha = \dfrac{ 2} 1$

Find the value of s and c:

$\text{ sin } \alpha = \dfrac{ s} { \sqrt{ 5 }}$

$\text{ cos } \alpha = \dfrac{ c} { \sqrt{ 5 }}$

Correct result:

s =  2
c =  1

#### Solution:

$\text{ tg} \ \alpha = \dfrac{ 2} { 1} = \dfrac{ a }{ b } \ \\ \text{ sin} \ \alpha = \dfrac{ a} {c} = \dfrac{ a} { \sqrt{ a^2+b^2}} = \dfrac{ 2 } { \sqrt{ 5 }}$
$\text{ cos} \ \alpha = \dfrac{ b} {c} = \dfrac{ b} { \sqrt{ a^2+b^2}} = \dfrac{ 1 } { \sqrt{ 5 }}$

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