8.1 Algebra 2 Trig Lesson Day 2

Label the sides given the trig ratio

Use Pythagorean theorem to find missing third side

Example 1:
In the following figure,  $\tan\left(x\right)=\frac{5}{12}$   , find the exact values  $\sin\left(x\right)$   of and  $\cos\left(x\right)$  .

Label the sides of the triangle with  $\tan\left(x\right)=\frac{5-opposite}{12-adjacent}$  

 $5^{2\ }+12^2=c^2$  

 $169=c^2$  

 $\sqrt{169}=13=c$  

 $\sin\left(x\right)=\frac{5}{13}$  

 $\cos\left(x\right)=\frac{12}{13}$