How do I calculate this? tan x=-2. sin x=? What is the formula?

How do I calculate this? tan x=-2. sin x=? What is the formula?

To start with x muxt be  in the 2nd or 4th quad because tanx is neg

this means that sinx can be neg or pos

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Now forget about the negative for the moment

Draw a right angled triangle.

Put x in one of the acute angles

tanx=2/1   so put 2 on the opposite side and 1 on the adjacent side.

Use Pythagoras' theorum to get the hypotenuse.   $${\sqrt{{\mathtt{5}}}}$$

So reading off the triangle  $$sinx=\pm\frac{2}{\sqrt5}$$

If tan x=-2, then either  y = 2 and x = -1, or y= -2 and x = 1.

And regardless, r = √5   ...... And sinx = y/r

So, either sin x = 2/√5  and x is a 2nd quadrant angle

Or, sin x = -2/√5     and x is a 4th quadrant angle