Question

Solve sin(3x)=1/4 for all X, X in degrees

Answer 1

ANSWER

$x=\frac{14.5\degree}{3}+120\degree n\:or\:x=\frac{165.5\degree}{3} +120\degree n$, for $n\ge 0$, where $n$ is an integer.

EXPLANATION

We want to solve the trigonometric equation;

$Sin(3x)=\frac{1}{4}$

Since sine ratio is positive, it means the argument,$(3x)$ is either the first quadrant or second quadrant.

This implies that;

$(3x)=arcsin(\frac{1}{4})$

$(3x)=14.5\degree$ in the first quadrant.

Or

$(3x)=180\degree-14.5\degree=165.5\degree$ in the second quadrant.

Since the sine function has a period of $360\degree$, The general solution is given by

$(3x)=14.5\degree+360\degree n\:or\:(3x)=165.5\degree +360\degree n$,for $n\ge 0$, where $n$ is an integer.

Dividing through by 3, we obtain the final solution to be;

$x=\frac{14.5\degree}{3}+120\degree n\:or\:x=\frac{165.5\degree}{3} +120\degree n$, for $n\ge 0$, where $n$ is an integer.