Sine, cosine, tangent and cotangent

2100005409

Level:

Which of the graphs is the graph of the function

f (x) = tg (x + \frac{π}{4})

2100005408

Level:

Which of the graphs is the graph of the function

f (x) = 2 - 2 \sin (x - \frac{π}{2})

2000005407

Level:

Determine the smallest period of the function

f (x) = 2 \cos 3 x

\frac{2}{3} π

2 π

\frac{1}{3} π

\frac{1}{4} π

2000005406

Level:

Which of the following statements is not true?

Functions

f (x) = \cos (x + \frac{π}{6})

and

g (x) = \sin (x - \frac{π}{6})

are equal.

Functions

f (x) = 2 - \cos 3 x

is even and its range of values is

[1; 3]

Functions

f (x) = \cos (x - \frac{π}{3})

and

g (x) = \sin (x + \frac{π}{6})

are equal.

Functions

f (x) = \cos x

and

g (x) = \sin (x + \frac{π}{2})

are equal.

2000005405

Level:

Which of the following statements is true?

All values of the function

f (x) = 2 - \cos x

are positive.

Function

f (x) = tg x

is increasing over the whole domain.

The smallest positive period of the function

f (x) = \sin 4 x

\frac{π}{4}

Function

f (x) = 1 + \sin x

is an odd function.

2000005404

Level:

Which of the following statements is true?

\sin 700^{\circ} = \sin 200^{\circ}

\cos 550^{\circ} = \cos 10^{\circ}

tg 20^{\circ} = tg (- 20^{\circ})

\cos 520^{\circ} = \cos 20^{\circ}

2000005402

Level:

What is the measure of the angle

x

x \in [0; 2 π)

, for which

\cos x = \frac{\sqrt{2}}{2}

and

tg x < 0

\frac{7}{4} π

\frac{1}{4} π

\frac{3}{4} π

\frac{5}{4} π

2000005403

Level:

What is the measure of the angle

x

x \in [0; 2 π)

, for which

tg x = - 1

and

\sin x > 0

\frac{3}{4} π

\frac{5}{4} π

\frac{1}{4} π

\frac{7}{4} π

2000005401

Level:

What is the measure of the angle

x

x \in [0; 2 π)

, for which

\sin x = - \frac{1}{2}

and

\cos x < 0

\frac{7}{6} π

\frac{5}{6} π

\frac{11}{6} π

\frac{1}{6} π

2000004204

Level:

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 2 x |

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Sine, cosine, tangent and cotangent

2100005409

2100005408

2000005407

2000005406

2000005405

2000005404

2000005402

2000005403

2000005401

2000004204

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