1003076706
Level:
B
How many values of the angle \( \alpha\in\left(0^{\circ}; 90^{\circ}\right)\cup\left(90^{\circ}; 180^{\circ}\right) \) satisfy the equation \( \mathrm{tg}\,\alpha = \mathrm{cotg}\,\alpha \)?
\( 2 \)
\( 1 \)
\( 0 \)
\( 4 \)
Sine, cosine, tangent and cotangent
1003076705
Level:
C
At which point \( x \in [12\pi;14\pi] \) has the function \( y = \sin x \) a maximum?
\( 12.5\pi \)
\( 13\pi \)
\( 12\pi \)
\( 13.5\pi \)
1003076704
Level:
C
Simplifying the expression \( 1 - (\cos x - \sin x)^2 \) we get:
\( \sin 2x \)
\( \cos 2x \)
\( 2 - \sin x \)
\( 1 - \sin 2x \)
1003076703
Level:
C
The expression \( \frac{\sin 2x}{\cos^2x } \) for $x\in(-\frac{\pi}{2}, \frac{\pi}{2})$ is equal to:
\( 2\,\mathrm{tg}\,x \)
\( \frac{\sin x}{1-\sin x} \)
\( \mathrm{tg}^2 x \)
\( \mathrm{tg}\,2x \)
1003076702
Level:
C
The domain of the expression \( \frac{\cos x}{1-\sin x} \) is the set:
\( \left\{x\in\mathbb{R}\colon x\neq\frac{\pi}2 + 2k\pi\text{, } k\in\mathbb{Z} \right\} \)
\( \mathbb{R} \)
\( \left\{x\in\mathbb{R}\colon x\neq\frac{3\pi}2 + 2k\pi\text{, } k\in\mathbb{Z} \right\} \)
\( \left\{x\in\mathbb{R}\colon x =k\pi\text{, } k\in\mathbb{Z} \right\} \)
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:
\( 1+\sqrt3 \)
\( 0 \)
\( \frac12 \)
\( 2 \)
1103076615
Level:
B
Choose the graph of the function \( f(x) = 3\cos\left(x + \frac{\pi}4 \right) \).
1103076614
Level:
B
Determine the graph of the function \( f(x)=0.5\sin(2x) + 1 \).
1103076613
Level:
B
Which of the graphs is graph of the function \( f(x)=2\cos(3x+\pi) \)?
1103076612
Level:
B
Identify the function shown in the graph.
\( f(x)=-\cos 2x \)
\( f(x)=\cos(-2x) \)
\( f(x)=-\sin 2x \)
\( f(x)=\sin(-2x) \)