Trigonometric equations and inequalities

2000006402

Level: 
A
An equation is solved graphically as shown in the picture. The solution is marked in red. Choose the corresponding equation.
\[ \mathrm{tg}\,{x} = {\sqrt{3}} \] \[ x \in [ 0 ;2\pi]\]
\[ \mathrm{tg}\,{x} = {\sqrt{3}} \] \[ x \in [ -\pi ;\pi]\]
\[ \mathrm{cotg}\,{x} = {\sqrt{3}} \] \[ x \in [ 0 ;2\pi]\]
\[ \mathrm{cotg}\,{x} = {\sqrt{3}} \] \[ x \in [ -\pi ;\pi]\]

2000006401

Level: 
A
An equation is solved graphically as shown in the picture. The solution is marked in red. Choose the corresponding equation.
\[ \mathrm{tg}\,{x} = \frac{\sqrt{3}}{3} \] \[ x \in ( -\pi ;\pi)\]
\[ \mathrm{tg}\,{x} = \frac{\sqrt{3}}{2} \] \[ x \in (-\pi ;\pi )\]
\[ \mathrm{cotg}\,{x} = \frac{\sqrt{3}}{2} \] \[ x \in ( -\pi ;\pi)\]
\[ \mathrm{cotg}\,{x} = \frac{\sqrt{3}}{3} \] \[ x \in ( -\pi ;\pi)\]

2000006304

Level: 
B
An inequality is solved graphically as shown in the picture. The solution is marked in red. Choose the corresponding inequality.
\[ \cos{x} > \frac{\sqrt{2}}{2} \] \[ x \in [ 0;2\pi ]\]
\[ \cos{x} > \frac{\sqrt{3}}{2} \] \[ x \in [ 0;2\pi ]\]
\[ \cos{x} \geq \frac{\sqrt{2}}{2} \] \[ x \in [ 0;2\pi ]\]
\[ \cos{x} \geq \frac{\sqrt{3}}{2} \] \[ x \in [ 0;2\pi ]\]

2000006303

Level: 
B
An inequality is solved graphically as shown in the picture. The solution is marked in red. Choose the corresponding inequality.
\[ \cos{x} < \frac{1}{2} \] \[ x \in [ 0;2\pi ]\]
\[ \cos{x} \leq \frac{\sqrt{2}}{2} \] \[ x \in [ 0;2\pi ]\]
\[ \cos{x} < \frac{\sqrt{2}}{2} \] \[ x \in [ 0;2\pi ]\]
\[ \cos{x} \leq \frac{1}{2} \] \[ x \in [ 0;2\pi ]\]

2000006302

Level: 
B
An inequality is solved graphically as shown in the picture. The solution is marked in red. Choose the corresponding inequality.
\[ \sin{x} < \frac{1}{2} \] \[ x \in [ 0;2\pi ]\]
\[ \sin{x} \leq \frac{\sqrt{2}}{2} \] \[ x \in [ 0;2\pi ]\]
\[ \sin{x} < \frac{\sqrt{2}}{2} \] \[ x \in [ 0;2\pi ]\]
\[ \sin{x} \leq \frac{1}{2} \] \[ x \in [ 0;2\pi ]\]

2000006301

Level: 
B
An inequality is solved graphically as shown in the picture. The solution is marked in red. Choose the corresponding inequality.
\[ \sin{x} \geq \frac{\sqrt{3}}{2} \] \[ x \in [ 0;2\pi ]\]
\[ \sin{x} \geq \frac{\sqrt{2}}{2} \] \[ x \in [ 0;2\pi ]\]
\[ \sin{x} > \frac{\sqrt{3}}{2} \] \[ x \in [ 0;2\pi ]\]
\[ \sin{x} > \frac{\sqrt{2}}{2} \] \[ x \in [ 0;2\pi ]\]

2000006204

Level: 
A
An equation is solved graphically as shown in the picture. The solution is marked in red. Choose the corresponding equation.
\[ \cos{x} = \frac{\sqrt{3}}{2} \] \[ x \in [ 0;2\pi ]\]
\[ \sin{x} = \frac{\sqrt{3}}{2} \] \[ x \in [ 0;2\pi ]\]
\[ \cos{x} = \frac{1}{2} \] \[ x \in [ 0;2\pi ]\]
\[ \sin{x} = \frac{1}{2} \] \[ x \in [ 0;2\pi ]\]

2000006203

Level: 
A
An equation is solved graphically as shown in the picture. The solution is marked in red. Choose the corresponding equation.
\[ \cos{x} = \frac{1}{2} \] \[ x \in [ 0;2\pi ]\]
\[ \sin{x} = \frac{\sqrt{3}}{2} \] \[ x \in [ 0;2\pi ]\]
\[ \cos{x} = \frac{\sqrt{3}}{2} \] \[ x \in [ 0;2\pi ]\]
\[ \sin{x} = \frac{1}{2} \] \[ x \in [ 0;2\pi ]\]

2000006202

Level: 
A
An equation is solved graphically as shown in the picture. The solution is marked in red. Choose the corresponding equation.
\[ \sin{x} = \frac{1}{2} \] \[ x \in [ 0;2\pi ]\]
\[ \sin{x} = \frac{\sqrt{3}}{2} \] \[ x \in [ 0;2\pi ]\]
\[ \cos{x} = \frac{\sqrt{3}}{2} \] \[ x \in [ 0;2\pi ]\]
\[ \cos{x} = \frac{1}{2} \] \[ x \in [ 0;2\pi ]\]

2000006201

Level: 
A
An equation is solved graphically as shown in the picture. The solution is marked in red. Choose the corresponding equation.
\[ \sin{x} = \frac{\sqrt{3}}{2} \] \[ x \in [ 0;2\pi ]\]
\[ \sin{x} = \frac{1}{2} \] \[ x \in [ 0;2\pi ]\]
\[ \cos{x} = \frac{\sqrt{3}}{2} \] \[ x \in [ 0;2\pi ]\]
\[ \cos{x} = \frac{1}{2} \] \[ x \in [ 0;2\pi ]\]