Angles, arcs and sectors
Principal Measure of an Angle
Submitted by michaela.bailova on Tue, 01/07/2025 - 17:33Conversion Between Degrees and Radians
Submitted by michaela.bailova on Fri, 12/13/2024 - 10:322010018504
Level:
A
In the interval \([ 0^{\circ };360^{\circ } ] \) find the angle coterminal with the angle \(900^{\circ }\).
\( 180^{\circ} \)
\(280^{\circ} \)
\(220^{\circ} \)
\( 300^{\circ} \)
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?
\( 1\)
\( 2\)
\( 0\)
\( 3\)