2000005407
Level:
B
Determine the smallest period of the function \(f(x)=2\cos 3x\).
\( \frac{2}{3}\pi\)
\( 2\pi\)
\( \frac{1}{3}\pi\)
\( \frac{1}{4}\pi\)
Sine, cosine, tangent and cotangent
2000005406
Level:
B
Which of the following statements is not true?
Functions \(f(x)=\cos\left(x+\frac{\pi}{6}\right)\) and \(g(x)=\sin\left(x-\frac{\pi}{6}\right)\) are equal.
Functions \(f(x)=2-\cos 3x\) is even and its range of values is \([ 1;3]\).
Functions \(f(x)=\cos\left(x-\frac{\pi}{3}\right)\) and \(g(x)=\sin\left(x+\frac{\pi}{6}\right)\) are equal.
Functions \(f(x)=\cos x\) and \(g(x)=\sin\left(x+\frac{\pi}{2}\right)\) are equal.
2000005405
Level:
B
Which of the following statements is true?
All values of the function \(f(x)=2-\cos x\) are positive.
Function \(f(x)=\mathrm{tg}\,x\) is increasing over the whole domain.
The smallest positive period of the function \(f(x)=\sin 4x\) is \(\frac{\pi}{4}\).
Function \(f(x)=1+\sin x\) is an odd function.
2000005404
Level:
B
Which of the following statements is true?
\( \sin 700^{\circ} = \sin 200^{\circ} \)
\( \cos 550^{\circ} = \cos 10^{\circ} \)
\( \mathrm{tg}\, 20^{\circ} = \mathrm{tg}\, (-20^{\circ}) \)
\( \cos 520^{\circ} = \cos 20^{\circ} \)
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 \(\frac{\sin 2x}{1 -\sin^2 x}\).
\( 2\ \mathrm{tg}\,x\)
\(\mathrm{tg}\,x\)
\( \mathrm{tg}^2\,x\)
\( 1-\mathrm{tg}\,x\)