Answer:
cot(x)=-sqrt(3)/3
Step-by-step explanation:
I'm going to use the Pythagorean Identity sin^2(x)+cos^2(x)=1 to find the sine value since cotangent value is the cosine value over sine value.
Plug in:
sin^2(x)+(-1/2)^2=1
Simplify:
sin^2(x)+1/4=1
Subtract 1/4 on both sidea:
sin^2(x)=3/4
Square root both sides:
sin(x)=sqrt(3)/2. [Sine is positive since x is in 2nd quadrant]
cot(x)=(-1/2)/(sqrt(3)/2))
cot(x)=-1/sqrt(3)
Rationalize denominator by multiplying by sqrt(3)/sqrt(3):
cot(x)=-sqrt(3)/3
cot(x)=
