5.05 Solving trigonometric equations 1
State whether the following equations have a solution:
\cos \theta - 4 = 0
9 \tan \theta + 4 = 0
State the number of solutions for \theta of the following equations in the domain \\ 0 \degree \lt \theta \lt 90 \degree.
\cos \theta = - \dfrac{1}{\sqrt{2}}
\sin \theta = - \dfrac{\sqrt{3}}{2}
\tan \theta = - 1
Solve the following equations for 0 \degree \leq \theta \leq 90 \degree:
\sin \theta = \dfrac{1}{\sqrt{2}}
\tan \theta = \sqrt{3}
\cos \theta = \dfrac{1}{2}
\sin \theta = \dfrac{\sqrt{3}}{2}
Solve the following equations for 0 \degree \leq \theta \leq 360 \degree:
\cos \theta = - \dfrac{1}{\sqrt{2}}
\cos \theta = \dfrac{1}{2}
\cos \theta = 0
\sin \theta = \dfrac{1}{2}
\sin \theta = 0
\sin \theta = - \dfrac{1}{\sqrt{2}}
\cos \theta = -\dfrac{1}{\sqrt{2}}
\sin \theta = - \dfrac{\sqrt{3}}{2}
\sin \theta = 1
\tan \theta = \sqrt{3}
\tan \theta = 0
\tan \theta = - \dfrac{1}{\sqrt{3}}
4 \tan \theta + 2 = - 2
8 \cos \theta - 4 = 0
2 \cos \theta + 4 = 3
8 \sin \theta - 4 \sqrt{2} = 0
\cos \theta = 0.7986
\sin \theta =0.6428
\tan \theta =0.7265
\sin \theta = 0.3584
\tan \theta = 2.2460
Solve the following equations for 0 \degree \leq \theta \leq 360 \degree:
\cos \theta = 0.9063
\cos \theta = - 0.7986
\sin \theta = - 0.6428
\sin \theta = 0.9336
\tan \theta = 0.7002
\tan \theta = - 0.7265
State the number of solutions for the following equations in the domain -90 \degree \lt \theta \lt 90 \degree:
\cos \theta = - \dfrac{1}{\sqrt{2}}
\cos \theta = - 0.914
State the number of solutions for the following equations in the domain 180 \degree \leq \theta \leq 360 \degree:
\sin \theta = - \dfrac{1}{\sqrt{2}}
\sin \theta = - 0.697
Solve the following equations for the given domain:
\cos \theta = \dfrac{1}{\sqrt{2}} for 0 \degree \lt \theta \lt 90 \degree
\sin \theta = - \dfrac{1}{2} for - 90 \degree \leq \theta \leq 90 \degree
\tan \theta = - 1 for - 180 \degree \leq \theta \leq 0 \degree
\tan \theta = 3 - 2 \tan \theta for 0 \degree \leq \theta \leq 180 \degree
Solve the following equations for the domain - 180 \degree \leq \theta \leq 180 \degree. Round your answer to two decimal places if necessary.
\cos \theta = - 0.831
\cos \theta = - \dfrac{1}{2}
\sin \theta = \dfrac{\sqrt{3}}{2}
\sin \theta = 0.238
\tan \theta = 1
\tan \theta = 1.237
Solve the following equations for the domain 360 \degree \leq \theta \leq 720 \degree. Round your answer to two decimal places if necessary.
\sin \theta = 0.3584
\tan \theta = 2.2460