Question

Find sin θ if cot θ = - 4 and cos θ < 0.

Answer 1

is it -17?

Answer 2

if cosine and cotangent are negative, it must be in the second quadrant.

Answer 3

cot(x) - tan(x)/(sin(x) + cos(x)
= (cot(x) -tan(x)(sin(x) - cos(x))/(sin^2(x) - cos^2(x)
=(cot(x)sin(x) - cot(x)cos(x) - tan(x)sin(x) + tan(x)cos(x))/(sin^2(x) - cos^2(x))
= cos(x) - cos^2(x)/sin(x) - sin^2(x)/cos(x) + sin(x))/(sin^2(x) - cos^2(x))
=( cos^2(x)/cos(x) - sin^2(x)/cos(x) + sin^2(x)/sin(x) - cos^2(x)/sin(x))/(sin^2(x) - cos^2(x))
= ((cos^2(x) - sin^2(x))/cos(x) - (cos^2(x) -sin^2(x))/sin(x)/(sin^2(x) - cos^2(x))
= (cos^2(x) -sin^2(x))(1/cos - 1/sin))/(sin^2(x) - cos^2(x))
= 1/sin(x) - 1/cos(x)
= csc(x) - sec(x)

Answer 4

I guess u r wrong..... @babydoll332

Answer 5

ohh ok so -1/4