1003076712
Level:
C
Let \( \sin x = a \) and \( \cos x = b \). Then \( \cos(2x) \) is equal to:
\( b^2-a^2 \)
\( 2b \)
\( 2ab \)
\( a^2-b^2 \)
C
1003076711
Level:
C
\( ABC \) is a triangle with side \( c = 27\,\mathrm{cm} \) and the angle \( \gamma = 78^{\circ} \). The radius of the circle circumscribed is:
\( 13.8\,\mathrm{cm} \)
\( 27.6\,\mathrm{cm} \)
\( 18.3\,\mathrm{cm} \)
\( 6.9\,\mathrm{cm} \)
1003076710
Level:
C
\( ABC \) is a triangle where the side \( b \) is \( 74\,\mathrm{cm} \) long and the angle \( \alpha = 60^{\circ} \). Find the length of its side \( c \) if you know that the area of the triangle is \( 720.9\,\mathrm{cm}^2 \).
\( 22.5\,\mathrm{cm} \)
\( 37.56\,\mathrm{cm} \)
\( 38.97\,\mathrm{cm} \)
\( 24.54\,\mathrm{cm} \)
1003076709
Level:
C
The area of an obtuse triangle is \( 2\,\mathrm{dm}^2 \). The lengths of sides containing the obtuse angle are \( 2\,\mathrm{dm} \) and \( 4\,\mathrm{dm} \). The measure of this angle is:
\( 150^{\circ} \)
\( 165^{\circ} \)
\( 155^{\circ} \)
\( 158^{\circ} \)
1003076708
Level:
C
The measures of the interior angles of a triangle are \( 30^{\circ} \), \( 45^{\circ} \) and \( 105^{\circ} \). The length of its longest side is \( 10\,\mathrm{cm} \). The length of its shortest side is:
\( 5.18\,\mathrm{cm} \)
\( 7.33\,\mathrm{cm} \)
\( 5.01\,\mathrm{cm} \)
\( 7.07\,\mathrm{cm} \)
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:
\( \left\{x\in\mathbb{R}\colon x\neq\frac{\pi}2 + 2k\pi\text{, } k\in\mathbb{Z} \right\} \)
\( \mathbb{R} \)
\( \left\{x\in\mathbb{R}\colon x\neq\frac{3\pi}2 + 2k\pi\text{, } k\in\mathbb{Z} \right\} \)
\( \left\{x\in\mathbb{R}\colon x =k\pi\text{, } k\in\mathbb{Z} \right\} \)
1103076611
Level:
C
The graph shown in the picture is graph of the function:
\( f(x)=\sin|x| \)
\( f(x)=|\sin x| \)
\( f(x)=|\cos x| \)
\( f(x)=\cos|x| \)