1003076507
Level:
B
For which \( x \in[0;\frac{\pi}2] \) is \( \sin x = \cos x \)?
\( \frac{\pi}4 \)
\( 0 \)
\( \frac{\pi}2 \)
\( \frac{\pi}3 \)
Sine, Cosine, Tangent, and Cotangent
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.
\( f(x)=-|\sin x|;\ x\in[-2\pi;2\pi] \)
\( f(x)=|\cos x|;\ x\in[-2\pi;2\pi] \)
\( f(x)=|-\sin x|;\ x\in[-2\pi;2\pi] \)
\( f(x)=-0.5\cdot\sin x;\ x\in[-2\pi;2\pi] \)
1003048506
Level:
B
Identify which of the following functions has the smallest period.
\( f(x)=(\cos(2x) )^2 \)
\( h(x)=\sin\bigl(\frac{x}{2}\bigr) \)
\( m(x)=\mathrm{tg}\,\bigl(\frac{x}{2}\bigr) \)
\( g(x)=(\mathrm{cotg}\, x)^2 \)
9000038910
Level:
B
Consider the function \(f\colon y =\mathop{\mathrm{cotg}}\nolimits x\).
In the following list identify the function which has the same graph as the graph of the
function \(f\).
\(k\colon y = -\mathop{\mathrm{tg}}\nolimits \left (x + \frac{\pi } {2}\right )\)
\(g\colon y = -\mathop{\mathrm{tg}}\nolimits x\)
\(b\colon y =\mathop{\mathrm{tg}}\nolimits \left (x + \frac{\pi } {2}\right )\)
\(h\colon y =\mathop{\mathrm{tg}}\nolimits \left (x - \frac{\pi } {2}\right )\)
\(m\colon y = -\mathop{\mathrm{tg}}\nolimits x - \frac{\pi } {2}\)