College Analytic Trigonometry

[CandiceC]

find tan(s) if cos(s)=-3/5 and tan(s)<0

I know how to solve this, but I don't know how to locate cos-3/5 on the unit circle

please help, thanks

 

[Deleted member 4993]

find tan(s) if cos(s)=-3/5 and tan(s)<0

I know how to solve this, but I don't know how to locate cos-3/5 on the unit circle

please help, thanks

's' will be in the 2nd or the 3rd quadrant (where base of the triangle in the unit circle will be negative)

However, according to your post the problem does not say (ask) anything about unit circle.

 

[HallsofIvy]

There are two points on the unit circle where $\displaystyle cos(s)= -3/5$. On the unit circle, "cos(s)" is the x coordinate of the point (x, y). Since the unit circle has equation $\displaystyle x^2+ y^2= 1$ if cos(s)= x= -3/5, then $\displaystyle \frac{9}{25}+ y^2= 1$ so $\displaystyle y^2= 1- \frac{9}{25}= \frac{16}{25}$ and $\displaystyle sin(s)= y= \pm \frac{4}{5}$. Now tangent is "sine over cosine" so we have either $\displaystyle \frac{\frac{4}{5}}{-\frac{3}{5}}= -\frac{4}{3}$ or $\displaystyle \frac{-\frac{4}{5}}{-\frac{3}{5}}= \frac{4}{3}$. Since we are told that tangent is negative, the first of those is the correct answer.