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.

How many solutions are there to the equation \(sinx = -0.9\) where \(0\leq \times \textless 360\)?

None

One

Two

How many solutions are there to the equation \(sinx = 2\) where \(0 \leq \times \textless 360\)?

Solve the equation \(sinx = 0.5\) where \(0 \leq \times \textless 360\).

\(x = 30^\circ\) and \(x =210^\circ\)

\(x = 30^\circ\) and \(x =150^\circ\)

\(x = 210^\circ\) and \(x = 330^\circ\)

Solve the equation \(cosx = -0.5\) where \(0\leq x\textless 2\pi\).

\(x=\frac{\pi }{3}\), \(x=\frac{2\pi }{3}\)

\(x=\frac{2\pi }{3}\), \(x=\frac{11\pi }{6}\)

\(x=\frac{2\pi }{3}\), \(x=\frac{4\pi }{3}\)

Solve the equation \(5cosx - 2=0\) where \(0\leq x\textless 360\).

\(x = 66.4^\circ\) and \(x = 293.6^\circ\)

\(x = 66.4^\circ\) and \(x = 336.4^\circ\)

\(x = 113.6 ^\circ\) and \(x = 246.4^\circ\)

Solve the equation \(\sqrt{2}cosx-1=0\) where \(0\leq x\textless\pi\)

\[x=\frac{\pi }{4}\]

\(x=\frac{\pi }{4}\), \(\frac{3\pi }{4}\)

\(x=\frac{\pi }{4}\), \(\frac{7\pi }{4}\)

Solve the equation \(2\cos3x+1=0\), where \(0\leq x\textless 360^\circ\)

\[x=40^\circ ,\,80^\circ\]

\[x=60^\circ,\,120^\circ,\,240^\circ\]

\[x=40^\circ,\,80^\circ,\,160^\circ,\,200^\circ,\,280^\circ,\,320^\circ\]

Solve the equation \(3\,cos\,x+1 = 0.766\), where \(0\leq x\leq 540^\circ\)

\[x = 94.5^\circ,\,265.5^\circ,\,454.5^\circ\]

\[x = 94.5^\circ,\,265.5^\circ\]

\[x = 85.5^\circ,\,274.5^\circ,\,445.5^\circ\]

Solve the equation \(6sin^{2}x+sin\,x-1=0\), where \(0\leq x\leq 2\pi\)

\[x=\frac{\pi }{6},\frac{5\pi }{6}\]

\[x=0.3,2.8,\frac{7\pi }{6},\frac{11\pi }{6}\]

\[x=\frac{7\pi }{6},\frac{11\pi }{6}\]

Solve the equation \(2\,cos (x+60)=\sqrt{3}\), where \(0\leq x\leq 360^\circ\)

\[x=270^\circ ,\,330^\circ\]

\[x =30^\circ ,\,330^\circ\]

\[x =150^\circ,\,210^\circ\]