Question

hi
please help me
if we have tan(x)=-2
so what is sin(x),cos(x) and cot(x) ?

Answer 1

sinx=-2 cox =1 cotx = 1/-2

Answer 2

If tan(x) = -2, we can immediately say cot(x) = -1/2
There are 2 values for sin(x) and 2 corresponding values for cos(x), depending on your quadrant (which is determined by the range).

Case I: 2nd Quadrant

By Pythagorean Theorem,
hypotenuse ^ 2 = (-2)^2 + 1^2
hypotenuse = sqrt(5)
sin(x) = 1/sqrt(5) and cos(x) = -2/sqrt(5)

Case II: 4th quadrant

sin(x) = -1/sqrt(5) and cos(x) = 2/sqrt(5)