Find sinX if tanX=-12/5

Question

Find sinX if tanX=-12/5 and cosX >0

Answer 1

Hi Amber,

 

First of all notice that CosX is positive, and tanX is negative. That means we are in the fourth quadrant. 

 

Furthermore SinX is negative in the fourth quadrant.

 

Now,we are given tanx = -12/5.  by definition, tanx means ratio of the opposite side of an angle to the adjacent side. If we label the opposite side as y and the adjacent side as x, we have: tangx = y/x = -12/5  so y=-12 and x=5

 

What we don't know is the length of the hypotenuse which we need for evaluating Sinx as Sin is the ratio of opposite side of an angle to the hypotenuse.  We can use Pythagorean Theorem to find the length of the hypotenuse.

 

h²= x²+y² => h² = (-12)² + (5²) = 144+25 = 169    so h=sqrt(169) = 13  

                                                                            where sqrt(169) means square root of 169

 

Now, Sinx = y/h = -12/13