Angles, arcs and sectors

1003023309

Level:

What angle sweeps the hour hand of a clock in

3

hours?

- 90^{\circ}

45^{\circ}

- 45^{\circ}

90^{\circ}

1003055101

Level:

How many different values of

θ

meet both conditions:

θ \in ⋃_{k \in Z} {\frac{3 π}{4} + 2 k π}, θ \in [- 2 π; 4 π]

3

4

5

2

1003055102

Level:

The measure of the angle

θ

meets the following conditions:

θ \in ⋃_{k \in Z} {\frac{2}{3} π + k \frac{π}{3}}, θ \in [- \frac{π}{2}; 2 π] .

Choose the smallest value of

θ

- \frac{π}{3}

- \frac{π}{2}

\frac{2}{3} π

\frac{π}{3}

1003055103

Level:

Find out for which

k \in Z

is true:

- \frac{11}{4} π = \frac{7}{4} π + k \frac{π}{2}

- 9

9

- 18

18

1003055104

Level:

The measures of given angles belong to the set

M

M = {120^{\circ} + k 360^{\circ}}, k \in {- 1; 0; 1} .

Determine their arithmetic mean.

120^{\circ}

420^{\circ}

- 120^{\circ}

- 420^{\circ}

1003055105

Level:

The measurements of angles

θ

form the set

M

M = {π + k \frac{2}{3} π}, k \in {- 2; - 1; 1; 2} .

Calculate their sum.

4 π

0

\frac{2}{3} π

- \frac{2}{3} π

1003055106

Level:

Given two angles

α = \frac{66}{15} π

and

β = \frac{*}{5} π

, which of the following numbers is to be substituted for

*

so that both angles take the same position on the unit circle?

2

1

0

3

1003055109

Level:

What is the maximum error that can be obtained by adding four angles, if the size of each of them is rounded to the nearest degree before the addition?

2^{\circ}

0^{\circ}

3^{\circ}

4^{\circ}

1003055110

Level:

How many times in

12

hours (from

0 : 00

11 : 59 : 59

) will the minute hand and the hour hand make an angle of

1

degree?

22

11

12

24

1003055201

Level:

12

hours (from

0 : 00

am to

11 : 59 : 59

am), how many times do the minute and the hour hand make an angle of

0

rad ?

11

22

12

24

Angles, arcs and sectors

1003023309

1003055101

1003055102

1003055103

1003055104

1003055105

1003055106

1003055109

1003055110

1003055201

Events

Akce

Interests

Zajímavosti

About portal

O portálu