Find sin and cot

Question

Find sin(theta) and cot(theta) is the terminal side of theta lies along the line y= -3x in quadrant 4.

Answer 1

In quadrant 4, sin is negative and cos is positive. Thus, x is positive and y is negative, and √(x^2+(-3x)^2)) = √(10x^2) = √10 x

Then, sin = y/√(x^2+y^2) = -3x/√(x^2+(-3x)^2)) = -3x/√10 x= -3√10 /10

cos = x/√(x^2+y^2) = x/√(x^2+(-3x)^2)) = x/√10 x = √10/10

cot = cos/sin = √10/10/(-3√10 /10) = -1/3