Sine, cosine, tangent and cotangent

Graphs of Trigonometric Functions II

Submitted by robert.marik on Sun, 11/25/2018 - 00:28

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}

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

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}

1003076707

Level:

How many values of the angle

α \in [0^{\circ}; 360^{\circ}]

satisfy the equation

\sin α = \cos α

2

1

0

3

1003076706

Level:

How many values of the angle

α \in (0^{\circ}; 90^{\circ}) \cup (90^{\circ}; 180^{\circ})

satisfy the equation

tg α = cotg α

2

1

0

4

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

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

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

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}

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Sine, cosine, tangent and cotangent

Graphs of Trigonometric Functions II

1003076712

1003076711

1003076709

1003076707

1003076706

1003076705

1003076704

1003076703

1003076702

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