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1003076709

Level:

The area of an obtuse triangle is

2 {dm}^{2}

. The lengths of sides containing the obtuse angle are

2 dm

and

4 dm

. The measure of this angle is:

150^{\circ}

165^{\circ}

155^{\circ}

158^{\circ}

1003076708

Level:

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 cm

. The length of its shortest side is:

5.18 cm

7.33 cm

5.01 cm

7.07 cm

1003076705

Level:

At which point

x \in [12 π; 14 π]

has the function

y = \sin x

a maximum?

12.5 π

13 π

12 π

13.5 π

1003076704

Level:

Simplifying the expression

1 - (\cos x - \sin x)^{2}

we get:

\sin 2 x

\cos 2 x

2 - \sin x

1 - \sin 2 x

1003076703

Level:

The expression

\frac{\sin 2 x}{\cos^{2} x}

for

x \in (- \frac{π}{2}, \frac{π}{2})

is equal to:

2 tg x

\frac{\sin x}{1 - \sin x}

{tg}^{2} x

tg 2 x

1003076702

Level:

The domain of the expression

\frac{\cos x}{1 - \sin x}

is the set:

{x \in R : x \neq \frac{π}{2} + 2 k π, k \in Z}

R

{x \in R : x \neq \frac{3 π}{2} + 2 k π, k \in Z}

{x \in R : x = k π, k \in Z}

1103076611

Level:

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 |

1103076610

Level:

The figure shows the graph of the function:

f (x) = \cos (- 2 x)

f (x) = - \cos 2 x

f (x) = | \cos 2 x |

f (x) = - | \cos 2 x |

1103076608

Level:

Identify the function shown in the graph.

f (x) = - \sin (- 2 x)

f (x) = - \sin 2 x

f (x) = | \sin 2 x |

f (x) = \sin | 2 x |

1003034403

Level:

In a group of

100

people,

60

people like swimming,

50

people like horse-riding,

36

people like cycling. Further,

16

people like swimming and horse riding,

19

people like swimming and cycling,

15

people like horse-riding and cycling. How many people in the group enjoy only one of these activities?

58

29

23

6

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