9000033802
Level:
B
Which of the numbers in the list is a period (not necessarily the smallest period) of the
function \(n\colon y =\mathop{\mathrm{tg}}\nolimits x\)?
\(3\pi \)
\(\frac{\pi }{2}\)
\(- \frac{\pi } {2}\)
\(\frac{3\pi }
{2}\)
Sine, cosine, tangent and cotangent
9000032101
Level:
A
Evaluate
\(\sin \left ( \frac{\pi }{2}\right )\).
\(1\)
\(-\frac{\sqrt{2}}
{2} \)
\(-\sqrt{3}\)
\(\sqrt{3}\)
\(\frac{\sqrt{2}}
{2} \)
\(\frac{\sqrt{3}}
{3} \)
9000033804
Level:
B
In the following list identify a true statement for the function
\(g\colon y =\sin x\),
\(x\in [ - 2\pi ;-\pi ] \).
The function \(g\)
is neither increasing nor decreasing.
The function \(g\)
is increasing.
The function \(g\)
is decreasing.
9000032102
Level:
A
Evaluate
\(\sin \left (0\right )\).
\(0\)
\(\frac{\sqrt{2}}
{2} \)
\(-\sqrt{3}\)
\(- 1\)
\(\sqrt{3}\)
\(-\frac{\sqrt{3}}
{3} \)
9000032012
Level:
A
Evaluate
\(\mathop{\mathrm{cotg}}\nolimits \left ( \frac{\pi }{3}\right )\).
\(\frac{\sqrt{3}}
{3} \)
\(-\frac{1}
{2}\)
\(\frac{\sqrt{2}}
{2} \)
\(-\sqrt{3}\)
\(-\frac{\sqrt{3}}
{3} \)
\(-\frac{\sqrt{2}}
{2} \)
9000032103
Level:
A
Evaluate
\(\sin \left (\frac{5\pi }
{2}\right )\).
\(1\)
\(-\frac{\sqrt{3}}
{3} \)
\(-\frac{\sqrt{2}}
{2} \)
\(\sqrt{3}\)
\(\frac{\sqrt{3}}
{3} \)
\(\frac{\sqrt{2}}
{2} \)
9000033803
Level:
B
In the following list identify a true statement about the function
\(f(x) =\sin x\), where
\(x\in \left [ -\frac{\pi }{2}; \frac{\pi } {2}\right ] \).
The function \(f\)
is increasing.
The function \(f\)
is decreasing.
The function \(f\)
is neither increasing nor decreasing.
The function \(f\) is non-increasing.
9000032001
Level:
A
Evaluate
\(\mathop{\mathrm{tg}}\nolimits \left ( \frac{\pi }{2}\right )\).
undefined
\(\frac{\sqrt{2}}
{2} \)
\(- 1\)
\(\frac{\sqrt{3}}
{3} \)
\(-\frac{\sqrt{3}}
{3} \)
\(-\sqrt{3}\)
9000032104
Level:
A
Evaluate
\(\sin \left (\frac{-3\pi }
{2} \right )\).
\(1\)
\(\frac{\sqrt{3}}
{3} \)
\(\sqrt{3}\)
\(-\sqrt{3}\)
\(-\frac{\sqrt{2}}
{2} \)
\(-\frac{\sqrt{3}}
{3} \)
9000032002
Level:
A
Evaluate
\(\mathop{\mathrm{tg}}\nolimits \left (0\right )\).
\(0\)
\(\sqrt{3}\)
\(\frac{\sqrt{3}}
{3} \)
\(\frac{\sqrt{2}}
{2} \)
\(1\)
\(-\frac{\sqrt{3}}
{3} \)