2010018504
Level:
A
In the interval \([ 0^{\circ };360^{\circ } ] \) find the angle coterminal with the angle \(900^{\circ }\).
\( 180^{\circ} \)
\(280^{\circ} \)
\(220^{\circ} \)
\( 300^{\circ} \)
Angles, arcs and sectors
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.
\( 135^{\circ} \)
\(225^{\circ} \)
\(-135^{\circ} \)
\( 45^{\circ} \)
2010018502
Level:
A
One of the angles \( \alpha \), \( \beta \), \( \gamma \), \( \delta \) takes the same position on the unit circle as the angle \( ASB \). Which of the angles \( \alpha \), \( \beta \), \( \gamma \), \( \delta \) it is?
\( \alpha = 135^{\circ} \)
\( \beta = -100^{\circ} \)
\( \gamma= -315^{\circ} \)
\( \delta= 210^{\circ} \)
2010018501
Level:
B
Which number \(k \in \mathbb{N}\) satisfies the equation \(\frac94 \pi = k\pi-\frac{k}4\pi\)?
\(3\)
\(2\)
\(5\)
\(4\)
2010007208
Level:
B
Given two angles \( \alpha= \frac{65}{15}\pi \) and \( \beta=\frac{*}{3}\pi \), which of the following numbers is to be substituted for \( * \) so that both angles take the same position on the unit circle?
\( 1\)
\( 2\)
\( 0\)
\( 3\)
2010007207
Level:
B
The measures of given angles belong to the set \( M \):
\[ M = \left\{ 150^{\circ} + k\,360^{\circ}\right\},\ k\in\{-1;0;1\}.\]
Determine their arithmetic mean.
\( 150^{\circ} \)
\( 90^{\circ} \)
\( -90^{\circ} \)
\( -150^{\circ} \)
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.)
\( \frac54\pi \)
\( 2\pi \)
\(0 \)
\( \frac34\pi \)
2010007205
Level:
A
Select the set that does not contain the measures of coterminal angles with an angle of radian measure \( \frac{\pi}4 \). (Two angles are coterminal if they are drawn in the standard position and both have their terminal sides in the same location.)
\( \left\{\frac54\pi;\, -\frac{21}4\pi \right\} \)
\( \left\{\frac94\pi;\, -\frac74\pi \right\} \)
\( \left\{\frac{17}4\pi;\, \frac{41}4\pi \right\} \)
\( \left\{\frac{33}4\pi;\, \frac{49}4\pi \right\} \)
2010007204
Level:
A
Which of the given degree values is of the angle coterminal to the angle of \( -1500^{\circ} \)? (Two angles are coterminal if they are drawn in the standard position and both have their terminal sides in the same location.)
\( 300^{\circ} \)
\( -300^{\circ} \)
\( 60^{\circ} \)
\( -120^{\circ} \)
2010007203
Level:
A
Select the measure of an angle that is coterminal to an angle of \( 70^{\circ} \). (Two angles are coterminal if they are drawn in the standard position and both have their terminal sides in the same location.)
\( 430^{\circ} \)
\( 360^{\circ} \)
\( 290^{\circ} \)
\( 860^{\circ} \)