Question

Determine the exact value if cot(3pi/4) using special triangles.

I don't understand how it could be 1/tan3pi/4 in a triangle....

Answer 1

for any x,

cot(x) = 1/tan(x)

3pi/4 is in Quadrant II, so draw the triangle.
x = -1
y = 1
cot(3pi/4) = x/y = -1/1 = -1

or, consider that
cot(pi-x) = -cot(x)
since cos(pi-x) = -cos(x)
and sin(pi-x) = sin(x)
so, cot(3pi/4) = cot(pi - pi/4) = -cot(pi/4)