Question

How do you solve the following equation `sin x = 0.25` in the interval [0, 2pi]?

Answer 1

`x_1=0.25 and x_2 = 2.89`

Explanation:

The easiest way to solve this type of problem is to plot the `sin` function and `f(x) = 0.25` on one graph (link to this here) and look for the intersections.

The graph shows two intersections: the principal value of `x`, labelled in the answer as `x_1`, and the other value of `x`, labelled in the answer as `x_2`. To find the principal value of `x`, we simply use the inverse `sin` function, `sin^-1(x)`:

`x_1=sin^-1(0.25)=0.252680255142 approx 0.25`

To find the other value of `x`, we subtract the principle value of `x` from `pi`:

`x_2=pi-0.252680255142=2.8889123984477932 approx 2.89`