Question

How do you solve `2sinx + 1 =0`?

Answer 1

`x = (11pi)/6, (7pi)/6`

Explanation:

To solve this equation, go about it as you would any other equation. Get the sin x all by itself.

`2 sin x +1 = 0`

`2 sin x = -1`

`sin x = -1/2`

Then, use the unit circle to find all radian values which have a y-coordinate of `-1/2`, since sin is the `y` value (as opposed to cos, which is the x value).

As you can see, the coordinates `(-sqrt(3)/2`, `-1/2)` and `(sqrt(3)/2, -1/2)` have `y` values (or `sin` values) of `-1/2`.

The radian correspondents of these coordinates are `(7pi)/6` and `(11pi)/6`, and those are your two answers.