Finding trig functions

Question

Find the values of tan(thetha) =3/4 and sin(thetha)<0 

 

What I dont understand is the  sin(thetha)<0 

Answer 1

Hi Alex:

 

As you may know, there are two angles between 0 and 360^o (0 and 2π radians) where tan(θ) = (+)3/4.  The sin(θ)<0 part is just meant to distinguish between those two angles.  You can read it as "solve for θ where tan(θ) = (+)3/4 and where sin(θ) is negative."  So the answer will be in a quadrant where tangent is positive and sine is negative.  This will identify one unique angle for your solution.

 

Hope this helps!