Sine, cosine, tangent and cotangent

9000038909

Level:

Consider the function

f : y = \sin (\frac{x}{2} + \frac{π}{2})

. In the following list identify the function which has the same graph as the graph of the function

f

g : y = \cos \frac{x}{2}

k : y = \cos (\frac{x}{2} + \frac{π}{2})

b : y = \cos (\frac{x}{2} - \frac{π}{2})

h : y = \cos (\frac{x}{2} - π)

m : y = \cos 2 x

9000038910

Level:

Consider the function

f : y = cotg x

. In the following list identify the function which has the same graph as the graph of the function

f

k : y = - tg (x + \frac{π}{2})

g : y = - tg x

b : y = tg (x + \frac{π}{2})

h : y = tg (x - \frac{π}{2})

m : y = - tg x - \frac{π}{2}

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}

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

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

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

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}

1003076711

Level:

A B C

is a triangle with side

c = 27 cm

and the angle

γ = 78^{\circ}

. The radius of the circle circumscribed is:

13.8 cm

27.6 cm

18.3 cm

6.9 cm

1003076712

Level:

Let

\sin x = a

and

\cos x = b

. Then

\cos (2 x)

is equal to:

b^{2} - a^{2}

2 b

2 a b

a^{2} - b^{2}

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 |

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Sine, cosine, tangent and cotangent

9000038909

9000038910

1003076702

1003076703

1003076704

1003076705

1003076709

1003076711

1003076712

1103076608

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