Sine, cosine, tangent and cotangent

9000033808

Level:

In the following list identify a true statement for the function

f : y = \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 maximum and a unique minimum on

I

The function

f

has a unique maximum and no minimum on

I

The function

f

has a unique minimum and no maximum on

I

9000033809

Level:

Find the parity (odd/even) of the function

k : y = - tg x

The function

k

is an odd function.

The function

k

is an even function.

The function

k

is neither an odd nor even function.

9000038901

Level:

Consider the function

f : y = A \cdot \sin (B \cdot x + C)

, with real nonzero parameters

A

B

and

C

. Which of the following operations makes the period of the function five times smaller?

Increase

B

by a factor

5

Increase

A

by a factor

5

Decrease

A

by a factor

5

Decrease

B

by a factor

5

Increase

C

by a factor

5

Decrease

C

by a factor

5

9000038902

Level:

Consider the function

f : y = A \cdot \sin (B \cdot x + C)

, with real nonzero parameters

A

B

and

C

. Which of the following operations makes the amplitude of the function five times bigger?

Decrease

A

by a factor

5

Increase

A

by a factor

5

Increase

B

by a factor

5

Decrease

B

by a factor

5

Increase

C

by a factor

5

Decrease

C

by a factor

5

9000038903

Level:

Find the minimal value of the parameter

D

which ensures that the function

f : y = D + 3 \cdot \sin x

is nonnegative.

D = 3

D = - 3

D = 6

D = - 6

D = 1

No solution.

9000038904

Level:

Consider function

f : y = \sin x

with domain restricted to

Dom (f) = R_{0}^{+}

. Identify the function which is defined on

[- 5; + \infty)

f (x + 5)

f (x - 5)

f (x) + 5

f (x) - 5

5 \cdot f (x)

9000038905

Level:

Identify the transformation which transforms the graph of the function

g (x) = \sin 3 x

to the graph of the function

f (x) = \sin (3 x + 5)

Shift of graph of

g

\frac{5}{3}

of a unit to the left.

Shift of graph of

g

5

units to the right.

Shift of graph of

g

5

units to the left.

Shift of graph of

g

3

units to the right.

Shift of graph of

g

3

units to the left.

Shift of graph of

g

\frac{5}{3}

of a unit to the right.

9000038906

Level:

Consider the function

f : y = tg x

. In the following list identify the nonnegative function.

None of the given functions is nonnegative.

A \cdot f (x)

, where

A \in (- \infty; 0)

A \cdot f (x)

, where

A \in (0; + \infty)

f (B \cdot x)

, where

B \in (0; + \infty)

f (x + C)

, where

C \in (- \infty; 0)

9000038907

Level:

Consider the function

f (x) = cotg x

with domain restricted to the interval

Dom (f) = (0; π)

. In the following list identify the function with domain

(0; \frac{π}{3})

f (3 \cdot x)

f (x - 3)

f (x + 3)

f (\frac{x}{3})

3 \cdot f (x)

9000038908

Level:

Consider the function

f : y = tg x

with domain restricted to the interval

Dom (f) = (\frac{π}{2}; \frac{3 π}{2})

. In the following list identify the function with domain

(0; π)

f (x + \frac{π}{2})

(\frac{π}{2}) \cdot f (x)

f (x - \frac{π}{2})

f (x) + \frac{π}{2}

f (x) - \frac{π}{2}

Sine, cosine, tangent and cotangent

9000033808

9000033809

9000038901

9000038902

9000038903

9000038904

9000038905

9000038906

9000038907

9000038908

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