Question 180062
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Find sin(B) and cot(B) if cos(B) = -1/4 and tan(B) > 0.
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        Calculations in the post by @HyperBrain are incorrect.

        In whole, his solution is total mess.


        For correct solution, see my post below.



<pre>
Since cos(B) is negative and tan(B) is positive (given), we conclude from it that 
angle B is in QIII.


In QIII sine is negative, so we write

    sin(B) = {{{-sqrt(1-cos^2(B))}}} = {{{-sqrt(1-(-1/4)^2)}}} = {{{-sqrt(1-1/16)}}} = {{{-sqrt(15)/4}}}.


Hence,  cot(B) = {{{cos(B)/sin(B)}}} = {{{((-1/4))/((-sqrt(15)/4))}}} = {{{1/sqrt(15)}}} = {{{sqrt(15)/15}}}.


<U>ANSWER</U>.  sin(B) = {{{-sqrt(15)/4}}},  cot(B) = {{{sqrt(15)/15}}}.
</pre>

Solved correctly.