2000005404
Level:
B
Which of the following statements is true?
\( \sin 700^{\circ} = \sin 200^{\circ} \)
\( \cos 550^{\circ} = \cos 10^{\circ} \)
\( \mathrm{tg}\, 20^{\circ} = \mathrm{tg}\, (-20^{\circ}) \)
\( \cos 520^{\circ} = \cos 20^{\circ} \)
Sine, cosine, tangent and cotangent
2000005402
Level:
B
What is the measure of the angle \(x\), \(x \in [ 0;2\pi)\), for which \(\cos x = \frac{\sqrt{2}}{2}\) and \(\mathrm{tg}\,x < 0 \)?
\( \frac{7}{4}\pi\)
\( \frac{1}{4}\pi\)
\( \frac{3}{4}\pi\)
\( \frac{5}{4}\pi\)
2000005403
Level:
B
What is the measure of the angle \(x\), \(x \in [ 0;2\pi)\), for which \(\mathrm{tg}\,x = -1\) and \(\sin x >0\)?
\( \frac{3}{4}\pi\)
\( \frac{5}{4}\pi\)
\( \frac{1}{4}\pi\)
\( \frac{7}{4}\pi\)
2000005401
Level:
B
What is the measure of the angle \(x\), \(x \in [ 0;2\pi)\), for which \(\sin x = -\frac{1}{2}\) and \(\cos x < 0\)?
\( \frac{7}{6}\pi\)
\( \frac{5}{6}\pi\)
\( \frac{11}{6}\pi\)
\( \frac{1}{6}\pi\)
2000004204
Level:
C
Choose the function that has its graph shown in the picture.
\( f(x)=2-|\sin x|\)
\( f(x)=2+|\sin x|\)
\( f(x)=|\sin x|-2\)
\( f(x)=|\sin 2x|\)
2100004203
Level:
C
Which of the graphs is the graph of the function \(f(x)=|1+\cos x|\)?
2000004202
Level:
C
On the interval \( (-\frac{\pi}{2};\frac{\pi}{2})\), simplify the expression \(\frac{\sin 2x}{1 -\sin^2 x}\).
\( 2\ \mathrm{tg}\,x\)
\(\mathrm{tg}\,x\)
\( \mathrm{tg}^2\,x\)
\( 1-\mathrm{tg}\,x\)
2000004201
Level:
C
On the interval \( (0;\pi)\), simplify the expression \(\frac{2\sin x + \sin 2x}{2\sin x -\sin 2x}\).
\(\frac{1+\cos x}{1-\cos x}\)
\(\frac{1-\cos x}{1+\cos x}\)
\( 1+\cos x\)
\( 1-\cos x\)
2000004102
Level:
A
Calculate the value of the expression \(\sin\left( {\frac{2}{3}\pi} \right) +2\sin\left( {\frac{5}{3}\pi} \right) - 3\sin\left( {\frac{4}{3}\pi} \right) \).
\( \sqrt{3}\)
\( -\sqrt{3}\)
\( \frac{\sqrt{3}}{2}\)
\(2 \sqrt{3}\)
2000004101
Level:
A
Calculate the value of the expression \(\sin{45^{\circ}} -2\sin{225^{\circ}} - 5\sin{135^{\circ}}\).
\(- \sqrt{2}\)
\( \sqrt{2}\)
\( -2\sqrt{2}\)
\(- \sqrt{3}\)