9000032113
Level:
A
Evaluate
\(\sin \left ( \frac{\pi }{6}\right )\).
\(\frac{1}
{2}\)
\(\frac{\sqrt{2}}
{2} \)
\(-\frac{1}
{2}\)
\(\frac{\sqrt{3}}
{2} \)
\(\sqrt{3}\)
\(0\)
Sine, cosine, tangent and cotangent
9000032114
Level:
A
Evaluate
\(\cos \left ( \frac{\pi }{6}\right )\).
\(\frac{\sqrt{3}}
{2} \)
\(\frac{\sqrt{2}}
{2} \)
\(-\frac{1}
{2}\)
\(-\frac{\sqrt{3}}
{2} \)
\(0\)
\(-\frac{\sqrt{2}}
{2} \)
2000005407
Level:
B
Determine the smallest period of the function \(f(x)=2\cos 3x\).
\( \frac{2}{3}\pi\)
\( 2\pi\)
\( \frac{1}{3}\pi\)
\( \frac{1}{4}\pi\)
1003048506
Level:
B
Identify which of the following functions has the smallest period.
\( f(x)=(\cos(2x) )^2 \)
\( h(x)=\sin\bigl(\frac{x}{2}\bigr) \)
\( m(x)=\mathrm{tg}\,\bigl(\frac{x}{2}\bigr) \)
\( g(x)=(\mathrm{cotg}\, x)^2 \)
1003076501
Level:
B
To which quadrant does the angle \( \alpha \) belong if \( \sin\alpha=0.8 \) and \( \cos\alpha < 0 \)?
II.
I.
III.
IV.
1003076502
Level:
B
To which quadrant does the angle \( \alpha \) belong if \( \sin\alpha< 0 \) and \( \cos\alpha < 0 \)?
III.
I.
II.
IV.
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.
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 \( 1 \).
1003076505
Level:
B
Choose the false statement:
\( \cos190^{\circ} > \cos240^{\circ} \)
\( \sin140^{\circ} >\sin190^{\circ} \)
\( \sin15^{\circ}>\sin210^{\circ} \)
\( \cos305^{\circ}>\cos300^{\circ} \)
1003076506
Level:
B
Find the smallest period of the function \( f(x)=\mathrm{tg}\,4x \):
\( \frac{\pi}4 \)
\( 4\pi \)
\( \pi \)
\( 2\pi \)