Trigonometric equations can be solved in degrees or radians using CAST and its period to find other solutions within the range, including multiple or compound angles and the wave function.
Solve the equation \(4\sin x^\circ - 3 = 0\), where \(0 \le x \textless 360\).
Solution
First rearrange the equation.
\(4\sin x^\circ - 3 = 0\)
\(4\sin x^\circ = 0 + 3\)
\(4\sin x^\circ = 3\)
\(\sin x^\circ = \frac{3}{4}\)
The graph of this function looks like this:
From the graph of the function, we can see that we should be expecting 2 solutions: 1 solution between \(0^\circ\) and \(90^\circ\) and the other between \(90^\circ\) and \(180^\circ\).
\(\sin x^\circ = \frac{3}{4}\)
Since this is sin and is positive this means that we will be in the two quadrants where the sine function is positive - the first and second quadrants.