A

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.
\[ \sin{x} = \frac{\sqrt{3}}{2} \] \[ x \in [ 0;2\pi ]\]
\[ \sin{x} = \frac{1}{2} \] \[ x \in [ 0;2\pi ]\]
\[ \cos{x} = \frac{\sqrt{3}}{2} \] \[ x \in [ 0;2\pi ]\]
\[ \cos{x} = \frac{1}{2} \] \[ x \in [ 0;2\pi ]\]

2000005910

Level: 
A
The regular heptagon is inscribed in a circle. Calculate the magnitudes of the interior angles of the chordal quadrilateral \(ACEG\). (See the picture.)
\( \alpha=4\cdot\frac{360^{\circ}}{14}\); \( \beta=3\cdot\frac{360^{\circ}}{14}\); \( \gamma=3\cdot\frac{360^{\circ}}{14}\); \( \delta=4\cdot\frac{360^{\circ}}{14}\)
\( \alpha=4\cdot\frac{360^{\circ}}{7}\); \( \beta=3\cdot\frac{360^{\circ}}{7}\); \( \gamma=3\cdot\frac{360^{\circ}}{7}\); \( \delta=4\cdot\frac{360^{\circ}}{7}\)
\( \alpha=4\cdot\frac{180^{\circ}}{14}\); \( \beta=3\cdot\frac{180^{\circ}}{14}\); \( \gamma=3\cdot\frac{180^{\circ}}{14}\); \( \delta=4\cdot\frac{180^{\circ}}{14}\)
\( \alpha=4\cdot\frac{360^{\circ}}{14}\); \( \beta=4\cdot\frac{360^{\circ}}{14}\); \( \gamma=3\cdot\frac{360^{\circ}}{14}\); \( \delta=3\cdot\frac{360^{\circ}}{14}\)

2000005909

Level: 
A
The regular octagon \(ABCDEFGH\) is inscribed in the circle. Calculate the magnitudes of the interior angles of the chordal quadrilateral \(HBCF\). (See the picture.)
\( \alpha=90^{\circ}\); \( \beta=112.5^{\circ}\); \( \gamma=90^{\circ}\); \( \delta=67.5^{\circ}\)
\( \alpha=90^{\circ}\); \( \beta=67.5^{\circ}\); \( \gamma=90^{\circ}\); \( \delta=67.5^{\circ}\)
\( \alpha=90^{\circ}\); \( \beta=122.5^{\circ}\); \( \gamma=80^{\circ}\); \( \delta=67.5^{\circ}\)
\( \alpha=90^{\circ}\); \( \beta=67.5^{\circ}\); \( \gamma=90^{\circ}\); \( \delta=112.5^{\circ}\)