Sin x, if cos x = ⅖, and tanx < 0.

Answer 1

If tan x < 0, then the angle is in either the 2nd or 4th quadrant. Since cos x is positive, we know it must be the 4th, therefore the sine must be negative. Since cos x = 2/5, you can set up a triangle with hypotenuse 5 and the adjacent side length 2. The remaining side length is sqrt(5² - 2²) = sqrt(21). Therefore

sin x = -sqrt(21)/5