7.04 Trigonometric equations
Find the size of the acute angle \theta in the following equations:
\cos \theta = \dfrac{1}{2}
\sin \theta = \dfrac{1}{\sqrt{2}}
\tan \theta = \sqrt{3}
\sin \theta = \dfrac{\sqrt{3}}{2}
\sin \theta = \dfrac{1}{2}
\tan \theta = \dfrac{1}{\sqrt{3}}
Solve the following equations for 0\degree \leq x \leq 90\degree:
\tan x = 1
\sin x = \dfrac{1}{2}
2 \cos x = 1
\cos x = \dfrac{\sqrt{3}}{2}
\cos x - 1 = 0
\sqrt{2} \sin x = 1
\sin x - 1 = 0
\sin x = \dfrac{\sqrt{3}}{2}
Solve the following equations for 0\degree \leq \theta \leq 90\degree:
2 \sin \theta = 2 \sqrt{3} \cos \theta
\tan \theta = 2 \sqrt{3} - \tan \theta
6 \sin \theta - 3 \sqrt{3} = 0
State whether the following equations have a solution:
\cos \theta - 4 = 0
9 \tan \theta + 4 = 0
State the number of solutions for \theta in the following equations:
\cos \theta = - \dfrac{1}{2} for 0 \degree < \theta < 180 \degree
\tan \theta = - 1 for 0 \degree < \theta < 90 \degree
\sin \theta = - \dfrac{1}{\sqrt{2}} for 0 \degree < \theta < 90 \degree
\sin \theta = \dfrac{\sqrt{3}}{2} for 0 \degree < \theta < 180 \degree
Solve the following equations for 0\degree \leq x \leq 360\degree:
\cos x = \dfrac{1}{2}
\sin x = \dfrac{1}{\sqrt{2}}
\tan x = \dfrac{1}{\sqrt{3}}
\sin x = - \dfrac{1}{\sqrt{2}}
Solve the following equations for 0 \degree \leq \theta \leq 360 \degree:
\cos \theta = - \dfrac{1}{\sqrt{2}}
\cos \theta = 0
\sin \theta = 0
\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}}
Solve the following equations for 0 \degree \leq \theta \leq 360 \degree:
4 \tan \theta + 2 = - 2
8 \cos \theta - 4 = 0
2 \cos \theta + 4 = 3
8 \sin \theta - 4 \sqrt{2} = 0
Find the value of y in the following equations:
\dfrac{5}{8} \cos y = \dfrac{5 \sqrt{2}}{16} for 0 \degree < y < 90 \degree
\dfrac{6}{2} \sin y = \dfrac{3 \sqrt{3}}{2} for 0 \degree < y < 180 \degree
\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 to the nearest 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
Estimate the solutions of the following equations for 0 \degree \leq x \leq 360 \degree using the graph of y = \sin x below:
\sin x = 0.6
\sin x = -0.2
\sin x = \dfrac{1}{10}
\sin x = -0.95
Estimate the solutions of the following equations for 0 \degree \leq x \leq 360 \degree using the graph of y = \cos x below:
\cos x = 0.1
\cos x = -0.2
\cos x = \dfrac{1}{4}
2 \cos x = -1.2
Estimate the solutions of the following equations for 0 \degree \leq x \leq 360 \degree using the graph of y = \tan x below:
\tan x = 0.5
\tan x = -3
\tan x = \dfrac{3}{2}
2 \tan x = -8