State the number of solutions for \theta of the equation \left(\sin \theta + \dfrac{\sqrt{3}}{2}\right) \left(\cos \theta + \dfrac{\sqrt{3}}{2}\right) = 0 for 0 \degree \lt \theta \lt 90 \degree.
Solve the following equations for 0 \degree \lt \theta \lt 90 \degree:
\left(\sin \theta - \dfrac{\sqrt{3}}{2}\right) \left(\cos \theta - \dfrac{1}{\sqrt{2}}\right) = 0
\left(\sin \theta + \dfrac{1}{\sqrt{2}}\right) \left(\tan \theta - \dfrac{1}{\sqrt{3}}\right) = 0
Solve the following equations for the given domain:
\left(\tan \theta - \dfrac{1}{\sqrt{3}}\right) \left(\cos \theta + \dfrac{1}{\sqrt{2}}\right) = 0 for 180 \degree \leq \theta \leq 270 \degree
\left(\sin \theta - \dfrac{1}{2}\right) \left(\cos \theta - \dfrac{1}{\sqrt{2}}\right) = 0 for 270 \degree \leq \theta \leq 360 \degree
\tan ^{2}\left(\theta\right) = \sqrt{3} \tan \theta for - 90 \degree \lt \theta \lt 90 \degree
2 \sin ^{2}\left(\theta\right) - \sin \theta = 0 for - 180 \degree \leq \theta \leq 180 \degree
Deborah is solving the equation 2 \sin^{2} \theta + 7 \sin \theta + 5 = 0. After some factorisation, she arrives at the pair of equations \sin \theta + 1 = 0 and 2 \sin \theta + 5 = 0. Which of the two equations has a solution?
Solve the following equations for 0 \degree \leq \theta \leq 360 \degree. Round your answer to one decimal place if necessary.
\tan ^{2}\left(\theta\right) - 2 \tan \theta + 1 = 0
4 \cos ^{3}\left(\theta\right) = 3 \cos \theta
5 \sin ^{2}\left(\theta\right) + 8 \sin \theta \cos \theta - 4 \cos ^{2}\left(\theta\right) = 0
7 \cos ^{2}\left(\theta\right) + 3 \cos \theta = 3
9 \sin ^{2}\left(x\right) + 5 \sin x = 3
\cos \theta \tan \theta = \cos \theta
8 \tan ^{2}\left(\theta\right) \cos \theta - 4 \tan ^{2}\left(\theta\right) = 0
Solve the equation 3 \sin \theta = 3 \sqrt{3} \cos \theta for 0 \lt \theta \lt 90 \degree.
Solve the following equations for 0 \degree \leq \theta < 360 \degree. Round your answers to the nearest degree if necessary.
2 \cos ^{2}\left(\theta\right) = 2 - \sin \theta
\sin ^{5}\left(\theta\right) \cos ^{3}\left(\theta\right) = 0
\cos ^{2}\left(\theta\right) - 8 \sin \theta \cos \theta + 3 = 0
\dfrac{1 - \tan ^{2}\left(\theta\right)}{1 + \tan ^{2}\left(\theta\right)} + \cos \theta = 0
Leigh is solving the equation 2 \sin^{2} \theta + 7 \sin \theta + 5 = 0. After some factorisation, she arrives at the pair of equations \sin \theta + 1 = 0 and 2 \sin \theta + 5 = 0.
Which of these two equations has a solution?
Hence determine the exact solutions to the equation, for 0 \leq \theta \leq 2\pi.
Winston is solving the equation \cos^{2} \theta - 5 \cos \theta + 4 = 0. After some factorisation, he arrives at the pair of equations \cos \theta - 4 = 0 and \cos \theta - 1 = 0.
Which of these two equations has a solution?
Hence determine the exact solutions to the equation, for 0 \leq \theta \leq 2\pi.
Find the exact solutions of the following equations where 0 \leq \theta \leq 2 \pi:
\sin ^{2}\left(x\right) - 6 \cos ^{2}\left(x\right) = 1