Sine, cosine, tangent and cotangent

2010016403

Level:

Identify the function shown in the graph.

f (x) = \cos 2 x

f (x) = - \cos 2 x

f (x) = \sin 2 x

f (x) = - \sin 2 x

2010016405

Level:

In the following list identify a true statement about the function

f (x) = \cos x

, where

x \in [- \frac{π}{2}; \frac{π}{2}]

The function

f

is neither increasing nor decreasing.

The function

f

is decreasing.

The function

f

is increasing.

The function

f

is increasing and decreasing.

2010016406

Level:

In the following list identify a true statement about the function

f (x) = \sin x

on the interval

I = (- \frac{π}{2}; \frac{π}{2})

The function

f

does not have a minimum or maximum on

I

The function

f

has a unique minimum and no maximum on

I

The function

f

has a unique maximum and no minimum on

I

The function

f

has a unique maximum and a unique minimum on

I

2010016407

Level:

Identify the transformation which transforms the graph of the function

g (x) = \cos (2 x)

to the graph of the function

f (x) = \cos (2 x - 1)

Shift of graph of

g

\frac{1}{2}

of a unit to the right.

Shift of graph of

g

\frac{1}{2}

of a unit to the left.

Shift of graph of

g

1

unit to the left.

Shift of graph of

g

1

unit to the right.

2010016408

Level:

Consider the function

f (x) = cotg x

with domain restricted to the interval

(0; π)

. In the following list identify the function with domain

(0; \frac{π}{2})

f (2 \cdot x)

f (x + 2)

f (x - 2)

f (\frac{x}{2})

2010016801

Level:

To which quadrant does the angle

φ

belong if

\cos φ = 0.8

and

\sin φ < 0

IV.

II.

III.

2010016802

Level:

Choose the true statement:

\sin 240^{\circ} < \sin 120^{\circ}

\cos 50^{\circ} < \cos 130^{\circ}

\sin 300^{\circ} < \sin 270^{\circ}

\cos 330^{\circ} < \cos 150^{\circ}

2010016803

Level:

The value of

\cos (- \frac{28 π}{3})

is the same as the value of

\cos \frac{4 π}{3}

\cos \frac{π}{3}

\cos (- \frac{7 π}{3})

\cos \frac{5 π}{3}

2010016804

Level:

How many

x

-intercepts has the graph of the function

f (x) = \sin 2 x

on the interval

[- π; 2 π]

7

5

8

6

2100005408

Level:

Which of the graphs is the graph of the function

f (x) = 2 - 2 \sin (x - \frac{π}{2})

Sine, cosine, tangent and cotangent

2010016403

2010016405

2010016406

2010016407

2010016408

2010016801

2010016802

2010016803

2010016804

2100005408

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