Question

find the exact value of
cot(11pi/6)
cos(11pi/6)
csc(11pi/6)

Answer 1

cot = adj /opp negative in quadrant 4
cos = adjacent/hyp positive in quadrant 4
csc= hyp /opposite negative in quadrant 4

Answer 2

thank you sooooo much

Answer 3

\[11\Pi/6\] Belongs to a certain family of angles.
The families are \[\Pi/4, \Pi/6, \Pi/3\]
So if you have a value such as \[58\Pi/6\]
then it belongs to the pi/6 family and it's sin,cos,csc,sec,tan would be the same as that of pi/6.


Those two triangles are important in such problems because they should help you find sine,cos,tan and so on of the families I named above.
So after you have the sin, cos or whatever you're looking for, check what quadrant the angle you had initially lies in.
So in the first quadrant, all(cos,sin,tan,csc,sec) are positive, in the second only sine is positive, in the 3rd tan is positive and in the 4th, only cos is positive.
Hope that helps