Question

What value of `x` in the interval `0°<=x<=180°` satisfies the equation `sqrt3 tanx+1=0`?

Answer 1

`x = 150^("o")`

Explanation:

`sqrt3 tan x + 1 = 0`

`sqrt3 tan x = -1`

`tan x = frac{-1}{sqrt3}`

Within the quadrants I and II of the unit circle, the only quadrant for which `tan x` would be negative is quadrant 2.

From looking at the unit circle, we can see that the ratio of `sinx` to `cosx` in quadrant II is `frac{(1/2)}{((-sqrt3 )/ 2)}` when `x` is `150^("o")`