If $sin theta = -5/13$ and $cos theta = -12/13$ , how do you find $cot theta$ ?

Question

11367 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-04-01T06:27:35

$cottheta=12/5$

We know that:

$tantheta=sintheta/costheta$

and

$cottheta=1/tantheta$

So we can plug in our values:

$color(white)=cot(theta)$

$=1/tan(theta)$

$=1/(sintheta/costheta)$

$=1/(sintheta/costheta)color(blue)(*costheta/costheta)$

$=1/(sintheta/color(red)cancelcolor(black)costheta)color(blue)(*costheta/color(red)cancelcolor(blue)costheta)$

$=1/sinthetacolor(blue)(*costheta)$

$=costheta/sintheta$

Now plug in our values:

$=(-12/13)/(-5/13)$

$=(-12/13)/(-5/13)color(blue)(*13/13)$

$=(-12/color(red)cancelcolor(black)13)/(-5/color(red)cancelcolor(black)13)color(blue)(*color(red)cancelcolor(blue)13/color(red)cancelcolor(blue)13)$

$=(-12)/(-5)color(blue)(*1/1)$

$=(-12)/(-5)$

$=(color(red)cancelcolor(black)-12)/(color(red)cancelcolor(black)-5)$

$=12/5$

That's the solution. Hope this helped!

If sin theta = -5/13sin theta = -5/13 and cos theta = -12/13cos theta = -12/13, how do you find cot thetacot theta?