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.
\( \frac34 \pi \)
\( \frac54 \pi \)
\( -\frac34 \pi \)
\( -\frac54 \pi \)

1103055107

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 southwest.
\( 225^{\circ} \)
\( 135^{\circ} \)
\( -225^{\circ} \)
\( -45^{\circ} \)

1003055102

Level: 
B
The measure of the angle \( \theta \) meets the following conditions: \[\theta\in\bigcup\limits_{k\in\mathbb{Z}}\left\{\frac23\pi+k\frac{\pi}3\right\},\ \theta\in\left[-\frac{\pi}2;2\pi\right].\] Choose the smallest value of $\theta$.
\( -\frac{\pi}3 \)
\( -\frac{\pi}2 \)
\( \frac23\pi \)
\( \frac{\pi}3 \)

9000045710

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