Question 1198891
<font color=black size=3>
Angle alpha is on the interval ]pi/2, pi[ which is equivalent to saying pi/2 < alpha < pi
Each endpoint is excluded. 


Because pi/2 < alpha < pi, this angle is in quadrant Q2, which is in the northwest corner.


In Q2 we have these facts:
cosine is negative
sine is positive
tangent is negative


cos(alpha) = -12/13 = adjacent/hypotenuse
adjacent = -12
hypotenuse = 13


Use the pythagorean theorem to find the opposite side is 5 units long.


opposite = 5
adjacent = -12
hypotenuse = 13


Then,
sin(alpha) = opposite/hypotenuse
sin(alpha) = <font color=red>5/13</font>
and
tan(alpha) = opposite/adjacent
tan(alpha) = 5/(-12)
tan(alpha) = <font color=red>-5/12</font>


Diagram:
{{{drawing(500,500,-18,2,-5,15,
graph(500,500,-18,2,-5,15,-100),
line(0,0,-12,5),
line(-12,5,-12,0),
line(-12,0,0,0),
locate(-15,4,"opposite"),
locate(-13,3,"5"),
locate(-7,-1,"adjacent"),
locate(-7,-2,"-12"),
locate(-6,4.5,"hypotenuse"),
locate(-6,3.5,"13"),
locate(-4,1.2,alpha),
locate(-17,-3,matrix(1,3,"Diagram","to","scale"))
)}}}
</font>