Angles, arcs and sectors

1103055108

Level: 
B
The figure shows a directional rosette that can be used to determine a marching angle. (The initial arm always faces north and the terminal arm determines the direction of the march, so the measure of the angle increases from north to east.) Give the radian measure of the marching angle if the march is directed southeast.
\( \frac34 \pi \)
\( \frac54 \pi \)
\( -\frac34 \pi \)
\( -\frac54 \pi \)

1103055205

Level: 
B
Given the square \( ABCD \), find the measures of all coterminal angles to the angle \( DCB \). (Two angles are coterminal if they are drawn in the standard position and both have their terminal sides in the same location.)
\( \frac{\pi}2+2k\pi \), \( k\in\mathbb{Z} \)
\( \frac{\pi}2+k\pi \), \( k\in\mathbb{Z} \)
\( -\frac{\pi}2+2k\pi \), \( k\in\mathbb{Z} \)
\( -\frac{\pi}2+k\pi \), \( k\in\mathbb{Z} \)

1103055206

Level: 
B
\( ABCD \) is a square, as it is shown in the picture. Find the measures of all the coterminal angles to the angle \( BDA \). (Two angles are coterminal if they are drawn in the standard position and both have their terminal sides in the same location.)
\( \frac74\pi+2k\pi \), \( k\in\mathbb{Z} \)
\( \frac4\pi+2k\pi \), \( k\in\mathbb{Z} \)
\( \frac4\pi+k\pi \), \( k\in\mathbb{Z} \)
\( -\frac74\pi+2k\pi \), \( k\in\mathbb{Z} \)

2010007206

Level: 
B
The radian measure of the angle \( \varphi \) is \( \frac{\pi}4 \). What is the sum of all the radian measures of the angles coterminal to \( \varphi \) from the interval \( [ -5\pi; 5\pi ] \)? (Two angles are coterminal if they are drawn in the standard position and both have their terminal sides in the same location.)
\( \frac54\pi \)
\( 2\pi \)
\(0 \)
\( \frac34\pi \)

2010018503

Level: 
B
The figure shows a directional rosette that can be used to determine a marching angle. (The initial arm always faces north, and the terminal arm determines the direction of the march, so the measure of the angle increases from north to east.) Give the degree measure of the marching angle if the march is directed southeast.
\( 135^{\circ} \)
\(225^{\circ} \)
\(-135^{\circ} \)
\( 45^{\circ} \)

9000045710

Level: 
B
Find the length \(l\) of a latitude at \(50^{\circ }\) N. (Use \(R\) for the radius of the Earth.)
\(l = 2\pi R\cos 50^{\circ }\)
\(l = 2\pi R\sin 50^{\circ }\)
\(l = 2\pi R\mathop{\mathrm{tg}}\nolimits 50^{\circ }\)
\(l = 2\pi R\mathop{\mathrm{cotg}}\nolimits 50^{\circ }\)