1103076613
Level:
B
Which of the graphs is graph of the function \( f(x)=2\cos(3x+\pi) \)?
Sine, cosine, tangent and cotangent
1103076614
Level:
B
Determine the graph of the function \( f(x)=0.5\sin(2x) + 1 \).
1103076615
Level:
B
Choose the graph of the function \( f(x) = 3\cos\left(x + \frac{\pi}4 \right) \).
2000005401
Level:
B
What is the measure of the angle \(x\), \(x \in [ 0;2\pi)\), for which \(\sin x = -\frac{1}{2}\) and \(\cos x < 0\)?
\( \frac{7}{6}\pi\)
\( \frac{5}{6}\pi\)
\( \frac{11}{6}\pi\)
\( \frac{1}{6}\pi\)
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 \(\sin x >0\)?
\( \frac{3}{4}\pi\)
\( \frac{5}{4}\pi\)
\( \frac{1}{4}\pi\)
\( \frac{7}{4}\pi\)
2000005404
Level:
B
Which of the following statements is true?
\( \sin 700^{\circ} = \sin 200^{\circ} \)
\( \cos 550^{\circ} = \cos 10^{\circ} \)
\( \mathrm{tg}\, 20^{\circ} = \mathrm{tg}\, (-20^{\circ}) \)
\( \cos 520^{\circ} = \cos 20^{\circ} \)
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.
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.
2010016402
Level:
B
Identify the function shown in the graph.
\( f(x) = -\cos\left(x+\frac{\pi}4\right)\)
\( f(x) = \cos\left(x+\frac{\pi}4\right)\)
\( f(x) = \sin\left(x+\frac{\pi}4\right)\)
\( f(x) = -\cos\left(x-\frac{\pi}4\right)\)