7.06 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
State the number of solutions for the equation \cot \theta = - 1 for 270 \degree \leq \theta \leq 360 \degree.
Solve the following equations for 0 \degree \leq \theta \leq 90 \degree. Round your answers to one decimal place.
\text{cosec } \theta = 2.645
\cot \theta = 2.867
Solve the following equations for 0 \degree \leq \theta \leq 360 \degree. Round your answer to two decimal places if necessary.
\text{cosec } \theta = 1.6831
\text{cosec } \theta = - 1.7998
2 \left(\text{cosec } \theta + 1\right) = 12 - 5 \text{cosec } \theta
\text{cosec } \theta = 2
\sec \theta = 2.6711
\sec \theta = - 2.2925
6 \sec \theta - 1 = 3 \sec \theta - 7
\sec \theta = 2
\cot \theta = 0.3488
\cot \theta = - 1.1757
\cot \theta = \dfrac{1}{\sqrt{3}}
Solve the following equations for the given domain. Round your answers to the nearest minute if necessary.
\dfrac{4 \sqrt{3}}{3} - \cot \theta = 3 \cot \theta for 0 \degree \leq \theta \leq 180 \degree
\text{cosec } \theta = \dfrac{2}{\sqrt{3}} for - 90 \degree \leq \theta \leq 90 \degree
\sec \theta = 2 for - 180 \degree \leq \theta \leq 0 \degree
5 \cot \theta + 6 = 9 \cot \theta - 2 for \\ 0 \degree \leq \theta \leq 360 \degree
\sec \theta = 1.4543 for 0 \degree \lt \theta \lt 90 \degree