1003076509
Level:
B
At which point \( x\in(2\pi; 4\pi) \) has the function \( f(x)=\cos x \) a minimum?
\(3\pi\)
\(2 \pi \)
\( 4\pi \)
\( 3.5\pi \)
Sine, cosine, tangent and cotangent
1003076508
Level:
B
For which \( \alpha\in[0;90^{\circ} ] \) is \( \mathrm{tg}\,\alpha = \mathrm{cotg}\,\alpha \)?
\( 45^{\circ} \)
\( 60^{\circ} \)
\( 35^{\circ} \)
\( 30^{\circ} \)
1003076507
Level:
B
For which \( x \in[0;\frac{\pi}2] \) is \( \sin x = \cos x \)?
\( \frac{\pi}4 \)
\( 0 \)
\( \frac{\pi}2 \)
\( \frac{\pi}3 \)
1003076506
Level:
B
Find the smallest period of the function \( f(x)=\mathrm{tg}\,4x \):
\( \frac{\pi}4 \)
\( 4\pi \)
\( \pi \)
\( 2\pi \)
1003076505
Level:
B
Choose the false statement:
\( \cos190^{\circ} > \cos240^{\circ} \)
\( \sin140^{\circ} >\sin190^{\circ} \)
\( \sin15^{\circ}>\sin210^{\circ} \)
\( \cos305^{\circ}>\cos300^{\circ} \)
1003076504
Level:
B
Choose the false statement:
The function \( f(x)= \mathrm{tg}\,x \) is even.
The function \( f(x)=\mathrm{cotg}\,x \) is decreasing on the interval \( (0;\pi) \).
The function \( f(x)=\sin x \) is bounded on its domain.
The values of function \( f(x)=\cos x \) always lie between \( -1 \) and \( 1 \).
1003076503
Level:
B
Choose the true statement that applies to each of the functions \( f(x)=\sin x \), \( g(x)=\cos x \), \( h(x)= \mathrm{tg}\,x \):
The function has infinitely many zero points.
The function is odd.
The function is bounded.
The function is simple.
1003076502
Level:
B
To which quadrant does the angle \( \alpha \) belong if \( \sin\alpha< 0 \) and \( \cos\alpha < 0 \)?
III.
I.
II.
IV.
1003076501
Level:
B
To which quadrant does the angle \( \alpha \) belong if \( \sin\alpha=0.8 \) and \( \cos\alpha < 0 \)?
II.
I.
III.
IV.
1103082703
Level:
C
Function \( f \) is given completely by the next graph. Identify which of the following statements is true.
\( f(x)=-|\sin x|;\ x\in[-2\pi;2\pi] \)
\( f(x)=|\cos x|;\ x\in[-2\pi;2\pi] \)
\( f(x)=|-\sin x|;\ x\in[-2\pi;2\pi] \)
\( f(x)=-0.5\cdot\sin x;\ x\in[-2\pi;2\pi] \)