Solve the equation \(\cos x-\sin x=1\), where \(0 \leq x \leq 2 \pi\)
\(x =0 \text { or } \dfrac{3 \pi}{2}\)
In the domain, \(0 \le \theta \le 2 \pi\), solve \(\sqrt{3} \cos \theta - \sin \theta =1\)
\(\theta=\dfrac{\pi}{6}, \dfrac{3 \pi}{2}\)
For \(0^\circ \le \theta \le 360^\circ \), solve \(2 \cos \theta +\sin \theta =\dfrac{\sqrt{5}}{2}\)
\(\theta = 86^\circ 34'\) or \( 326^\circ 34'\)
For \(0^\circ \le \theta \le 360^\circ \), solve \(8 \cos \theta - 6 \sin \theta =7\)
\(\theta=8^\circ 42'\) or \(277^\circ 34'\)
Solve \(3 \cos 3 x-4 \sin 3 x=5\) for \(0 \leq x \leq \dfrac{2 \pi}{3}\)
\(x=\dfrac{2 \pi}{3}-\dfrac{1}{3} \tan ^{-1}\left(\dfrac{4}{3}\right)\text{ or 1.79}\)
In the domain, \(0 \le \theta \le 2\pi \), solve \(\cos \theta + \sin \theta = 1\)
\(0,\,\dfrac{\pi }{2},\,2\pi \)
In the domain, \( - \pi \le x \le \pi \), solve \(\cos x + \sqrt 3 \sin x = 2\)
\(x = \dfrac{\pi }{3}\)
In the domain \(0 \le x \le 2\pi \), solve \({\rm{3}}\sin x - \sqrt 3 \cos x = \sqrt 3 \)
\(x = \dfrac{\pi }{3}\) or \(\pi\)
In the domain \( - \pi \le \theta \le \pi \), solve \({\rm{cos}}\theta - \sqrt 3 \sin \theta = 2\)
\(\theta = - \dfrac{\pi }{3}\)
In the domain \(0 \le x \le 2\pi \), solve \(3\sin x + 4\cos x = 1\)
\(x = 2.01,\,\,5.55\)
For \( - \pi \le x \le \pi \), solve \(\sqrt 3 \cos x - \sin x = 1\)
\(x = \dfrac{\pi }{6}\) or \(x =- \dfrac{\pi }{2}\)
For \(0^\circ \le x \le 360^\circ \), solve \(4\sin x + 3\cos x = 5\)
\(x = 53^\circ 8'\)
For \(0 \le x \le 2\pi \), solve \(\sin x - \cos x = 1\)
\(\dfrac{\pi }{2},\pi \)
In the domain \(0 \le x \le 2\pi \), solve \(\sin x - \sqrt 3 \cos x = 2\)
\(x = \dfrac{{5\pi }}{6}\)
