If cos ⁡x=−1/2, and 90°<x<180°, find Sin X and Cot X

Question

I need this for a test please help T-T with work please

Answer 1

x = 130 or 2pi/3 in quadrant II (ignore 240 or 4pi/3 in quadrant III)

reference angle = 60 degrees, it forms a right triangle sides -1 sqr3 2

hypotenuse = sqr(1+3) =sqr4 = 2

sin130 = opposite side/hypotenuse sqr3/2 = about 0.866

cot130 = -1/sqr3 = -sqr3/3 = about -0.57735

or just use a calculator with trig functions.