1103109304
Level:
B
Choose the figure in which the points marked in black correspond to the roots of the equation \( x^5 + 1 = 0 \).
B
1103109303
Level:
B
Consider an equation \( x^n+b=0 \), where \( n \) is a positive integer and \( b \) is a real number. The points that correspond to the roots of the equation are marked in the figure as black points. Find the equation.
\( x^8 - 256 = 0 \)
\( x^8 + 256 = 0 \)
\( x^4 + 16 = 0 \)
\( x^4 - 16 = 0 \)
\( x^6 - 64 = 0 \)
\( x^6 + 64 = 0 \)
1003109302
Level:
B
Consider the equation \( x^4 - 81 = 0 \). Find the product of all its roots in the set of complex numbers.
\( -81 \)
\( 81 \)
\( -3 \)
\( 3 \)
\( 0 \)
1003109301
Level:
B
Consider the equation \( x^4 + 81 = 0 \). Find the sum of all its roots in the set of complex numbers.
\( 0 \)
\( 3 \)
\( -3 \)
\( 81 \)
\( - 81 \)
1003076515
Level:
B
By simplifying the expression \( \sin\left(\frac{\pi}2 - x \right) \) we get:
\( \cos x \)
\( \sin x \)
\( -\sin x \)
\( -\cos x \)
1003076514
Level:
B
By simplifying the expression \( \cos\left( \frac{\pi}2 - x \right) \) we get:
\( \sin x \)
\( \cos x \)
\( -\sin x \)
\( -\cos x \)
1003076513
Level:
B
If two of the values of \( \sin\alpha \), \( \cos\alpha \), \( \mathrm{tg}\alpha\) and \( \mathrm{cotg}\alpha \) are negative, then \( \alpha \) belongs to the interval
\( \left(\pi, \frac{3\pi}2 \right) \).
\( \left(0, \frac{\pi}2 \right) \).
\( \left(\frac{\pi}2, \pi\right) \).
\( \left( \frac{3\pi}2, 2\pi \right) \).
1003076512
Level:
B
The value of \( \sin\left(-\frac{53\pi}6\right) \) is the same as the value of
\( \sin\frac{7\pi}6 \).
\( \sin\frac{\pi}6 \).
\( \sin\frac{5\pi}6 \).
\( \sin\left( -\frac{11\pi}6 \right) \).
1003076511
Level:
B
If \( \mathrm{tg}\,x = 1 \), then \( \mathrm{cotg}\,x \) equals:
\( 1 \)
\( 0 \)
\( -1 \)
\( 0.5 \)
1003076510
Level:
B
If the angle \( \alpha\in[0,90^{\circ}] \) and \( \sin\alpha = 0.5 \), then \( \cos \alpha \) is equal to:
\( \frac{\sqrt3}2 \)
\( -\frac{\sqrt{3}}2 \)
\( -\frac12 \)
\( \frac12 \)