Draw the horizontal line \(y = 0.5\). The line \(y = 0.5\) crosses the graph of \(y = \sin{x}\) four times in the interval \(-360^\circ \leq \theta \leq 360^\circ\) so there are four solutions.

Tom Werner / Getty Images A sine wave is a geometric waveform that oscillates (moves up, down, or side-to-side) periodically and is defined by the function y = sin x. In other words, it is an s ...

2. Determine the roots of the equation \(\sqrt 5 \sin x + 2\cos x = 0\) in the interval \(0 \le x \le 2\pi\) 3. Sketch the graph of \(y = \sqrt 5 \sin x + 2\cos x\) for \(0 \le x \le 2\pi\) 4.

With static graphs and equations, it's possible to get a handle on the rules of what various functions do and mean. However, it's still hard to get an intuitive sense of the relationship between ...