1003076701
Level:
A
The value of the expression \( 3\cos\frac{\pi}2 - 3\sin\pi + 2\left(\cos\frac{\pi}3 - \sin\frac{4\pi}3 \right) \) is:
\( 1+\sqrt3 \)
\( 0 \)
\( \frac12 \)
\( 2 \)
Sine, cosine, tangent and cotangent
2000004101
Level:
A
Calculate the value of the expression \(\sin{45^{\circ}} -2\sin{225^{\circ}} - 5\sin{135^{\circ}}\).
\(- \sqrt{2}\)
\( \sqrt{2}\)
\( -2\sqrt{2}\)
\(- \sqrt{3}\)
2000004102
Level:
A
Calculate the value of the expression \(\sin\left( {\frac{2}{3}\pi} \right) +2\sin\left( {\frac{5}{3}\pi} \right) - 3\sin\left( {\frac{4}{3}\pi} \right) \).
\( \sqrt{3}\)
\( -\sqrt{3}\)
\( \frac{\sqrt{3}}{2}\)
\(2 \sqrt{3}\)
2010016805
Level:
A
The value of the expression \( 3\cos\frac{\pi}4 - 3\sin\frac{\pi}4 + 2\left(\cos\frac{\pi}3 - \sin\frac{\pi}6 \right) \) is:
\( 0\)
\( \sqrt2\)
\( 1\)
\( \frac12\)
9000032001
Level:
A
Evaluate
\(\mathop{\mathrm{tg}}\nolimits \left ( \frac{\pi }{2}\right )\).
undefined
\(\frac{\sqrt{2}}
{2} \)
\(- 1\)
\(\frac{\sqrt{3}}
{3} \)
\(-\frac{\sqrt{3}}
{3} \)
\(-\sqrt{3}\)
9000032002
Level:
A
Evaluate
\(\mathop{\mathrm{tg}}\nolimits \left (0\right )\).
\(0\)
\(\sqrt{3}\)
\(\frac{\sqrt{3}}
{3} \)
\(\frac{\sqrt{2}}
{2} \)
\(1\)
\(-\frac{\sqrt{3}}
{3} \)
9000032003
Level:
A
Evaluate
\(\mathop{\mathrm{tg}}\nolimits \left (\frac{5\pi }
{2}\right )\).
undefined
\(1\)
\(- 1\)
\(\sqrt{3}\)
\(\frac{\sqrt{2}}
{2} \)
\(-\frac{\sqrt{3}}
{3} \)
9000032004
Level:
A
Evaluate
\(\mathop{\mathrm{tg}}\nolimits \left (-\frac{3\pi }
{2}\right )\).
undefined
\(0\)
\(1\)
\(-\frac{\sqrt{3}}
{3} \)
\(- 1\)
\(\frac{\sqrt{3}}
{3} \)
9000032005
Level:
A
Evaluate
\(\mathop{\mathrm{cotg}}\nolimits \left ( \frac{\pi }{2}\right )\).
\(0\)
\(-\sqrt{3}\)
\(-\frac{\sqrt{2}}
{2} \)
\(\sqrt{3}\)
\(\frac{\sqrt{2}}
{2} \)
\(1\)
9000032006
Level:
A
Evaluate
\(\mathop{\mathrm{cotg}}\nolimits \left (0\right )\).
undefined
\(-\sqrt{3}\)
\(-\frac{\sqrt{2}}
{2} \)
\(\frac{\sqrt{3}}
{3} \)
\(-\frac{\sqrt{3}}
{3} \)
\(\frac{\sqrt{2}}
{2} \)