1103076610
Level:
C
The figure shows the graph of the function:
\( f(x)=\cos(-2x) \)
\( f(x)=-\cos 2x \)
\( f(x)=|\cos 2x| \)
\( f(x)=-|\cos 2x| \)
Sine, cosine, tangent and cotangent
1103076611
Level:
C
The graph shown in the picture is graph of the function:
\( f(x)=\sin|x| \)
\( f(x)=|\sin x| \)
\( f(x)=|\cos x| \)
\( f(x)=\cos|x| \)
1103082703
Level:
C
Function \( f \) is given completely by the next graph. Identify which of the following statements is true.
\( f(x)=-|\sin x|;\ x\in[-2\pi;2\pi] \)
\( f(x)=|\cos x|;\ x\in[-2\pi;2\pi] \)
\( f(x)=|-\sin x|;\ x\in[-2\pi;2\pi] \)
\( f(x)=-0.5\cdot\sin x;\ x\in[-2\pi;2\pi] \)
2000004201
Level:
C
On the interval \( (0;\pi)\), simplify the expression \(\frac{2\sin x + \sin 2x}{2\sin x -\sin 2x}\).
\(\frac{1+\cos x}{1-\cos x}\)
\(\frac{1-\cos x}{1+\cos x}\)
\( 1+\cos x\)
\( 1-\cos x\)
2000004202
Level:
C
On the interval \( (-\frac{\pi}{2};\frac{\pi}{2})\), simplify the expression \(\frac{\sin 2x}{1 -\sin^2 x}\).
\( 2\ \mathrm{tg}\,x\)
\(\mathrm{tg}\,x\)
\( \mathrm{tg}^2\,x\)
\( 1-\mathrm{tg}\,x\)
2000004204
Level:
C
Choose the function that has its graph shown in the picture.
\( f(x)=2-|\sin x|\)
\( f(x)=2+|\sin x|\)
\( f(x)=|\sin x|-2\)
\( f(x)=|\sin 2x|\)
2010016401
Level:
C
Identify the function shown in the graph.
\( f(x) = 2\sin x\)
\( f(x) = -2\sin x\)
\( f(x) = |2\sin x|\)
\( f(x) = |\sin x|\)
2010016404
Level:
C
Function \( f \) is given completely by the next graph. Identify which of the following statements is true.
\( f(x)=|-\cos x|;\ x\in [ -2\pi;2\pi ]\)
\( f(x)=-|\cos x|;\ x\in [ -2\pi;2\pi ]\)
\( f(x)=|\sin x|;\ x\in [ -2\pi;2\pi ]\)
\( f(x)=-|\sin x|;\ x\in [ -2\pi;2\pi ]\)
2010016806
Level:
C
The domain of the expression \( \frac{\cos^2 x}{1+\sin x} \) is the set:
\( \left\{x\in\mathbb{R}\colon x\neq\frac{3\pi}2 + 2k\pi,\ k\in\mathbb{Z} \right\} \)
\( \mathbb{R}\)
\( \left\{x\in\mathbb{R}\colon x\neq\frac{\pi}2 + 2k\pi,\ k\in\mathbb{Z} \right\} \)
\( \left\{x\in\mathbb{R}\colon x\neq \pi + 2k\pi,\ k\in\mathbb{Z} \right\} \)
2010016807
Level:
C
The expression \( \frac{\sin x-\sin^3 x}{\cos x-\cos^3 x } \) for $x\in\left(0;\frac{\pi}{2}\right)$ is equal to:
\( \mathrm{cotg}\,x \)
\( \mathrm{tg}\,x \)
\( \sin x \cdot \cos x \)
\( 2\,\mathrm{tg}\,x \)