Angles, arcs and sectors

1003055207

Level: 
B
The measure of the angle \( \theta \) is \( \frac{\pi}4 \). How many coterminal angles to \( \theta \) have the measure from the interval \( [ -4\pi;6\pi ] \)? (Two angles are coterminal if they are drawn in the standard position and both have their terminal sides in the same location.)
\( 5 \)
\( 6 \)
\( 7 \)
\( 8 \)

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.)
\( \frac74\pi+2k\pi \), \( k\in\mathbb{Z} \)
\( \frac4\pi+2k\pi \), \( k\in\mathbb{Z} \)
\( \frac4\pi+k\pi \), \( k\in\mathbb{Z} \)
\( -\frac74\pi+2k\pi \), \( k\in\mathbb{Z} \)

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.)
\( \frac{\pi}2+2k\pi \), \( k\in\mathbb{Z} \)
\( \frac{\pi}2+k\pi \), \( k\in\mathbb{Z} \)
\( -\frac{\pi}2+2k\pi \), \( k\in\mathbb{Z} \)
\( -\frac{\pi}2+k\pi \), \( k\in\mathbb{Z} \)

1003055204

Level: 
B
If the minute hand determines the initial arm and if the hour hand determines the terminal arm of an angle in the clockwise direction, what is the radian measure of the angle between the two hands at \( 5\!:\!00 \)?
\( -\frac56\pi \)
\( -\frac76\pi \)
\( -\frac34\pi \)
\( -\frac23\pi \)

1003055203

Level: 
B
Let the minute hand determine the initial arm and let the hour hand determine the terminal arm of an angle in the clockwise direction. What is the radian measure of the angle between the two hands at \( 11\!:\!30 \)?
\( -\frac{11}{12}\pi \)
\( -\frac56\pi \)
\( -\frac76\pi \)
\( -\frac{13}{12}\pi \)

1003055202

Level: 
B
Choose a statement that is not true for the angle \( \theta \) that the minute hand as an initial arm makes with the hour hand as a terminal arm in the clockwise direction.
\( 4\!:\!30 \), \( \theta = -300^{\circ}30' \)
\( 10\!:\!45 \), \( \theta = -52^{\circ}30' \)
\( 7\!:\!45\), \( \theta = -322^{\circ}30' \)
\( 3\!:\!15 \), \( \theta = -7^{\circ}30' \)