Use the Pythagorean Theorem Identities. Find sinx if cotx=−√3/2 and cosx<0

Answer 1

Since cotx < 0 (so tanx < 0) and cosx < 0, we are in QII (ie π/2 < x < π ), which means sinx > 0.

We could draw a right triangle in the 2nd quadrant with adjacent leg = - √3 and opposite leg = 2. We could then use pythag thm to find hypotenuse and sinx, but the question specifies that we should instead use a pythagorean trig id. So ...

1 + cot²x = csc²x

1 + 3/4 = csc²x

cscx = √7/2 and sinx = 2/√7 = 2√7/7