Trigonometric equations and inequalities

1003086108

Level:

The solution set of the equation

1 + \sin x \cdot \cos 2 x = \sin x + \cos 2 x

for

x \in R

is:

⋃_{k \in Z} {\frac{π}{2} + 2 k π; k π}

⋃_{k \in Z} {\frac{π}{2} + 2 k π}

⋃_{k \in Z} {k π}

⋃_{k \in Z} {2 k π}

1003086107

Level:

The solution set of the equation

2 {tg}^{2} x + 4 \cos^{2} x = 7

for

x \in R

is:

⋃_{k \in Z} {\frac{π}{3} + k π; \frac{2 π}{3} + k π}

⋃_{k \in Z} {\frac{π}{3} + 2 k π; \frac{2 π}{3} + 2 k π}

⋃_{k \in Z} {\frac{π}{3} + k π}

⋃_{k \in Z} {\frac{2 π}{3} + k π}

1003086106

Level:

The solution set of the equation

\sin 2 x = \cos 3 x \cdot \sin 2 x

for

x \in [0^{\circ}; 180^{\circ}]

is:

{0^{\circ}; 90^{\circ}; 120^{\circ}; 180^{\circ}}

{90^{\circ}; 120^{\circ}; 180^{\circ}}

{90^{\circ}; 180^{\circ}}

{0^{\circ}; 90^{\circ}}

1003086105

Level:

How many solutions does the equation

2 \cos^{2} x - \cos x - 1 = 0

have in the interval

[- π; 3 π]

6

4

2

3

1003086104

Level:

Which of the following equations has exactly two solutions in the interval

[0; π]

3 \sin x - 2 = 0

2 \sin x - 3 = 0

3 \cos x + 2 = 0

3 \sin x + 2 = 0

1003086103

Level:

The solution set of the equation

2 \sin x + tg x = 0

x \in R

is:

⋃_{k \in Z} {k π; \frac{2 π}{3} + 2 k π; \frac{4 π}{3} + 2 k π}

⋃_{k \in Z} {2 k π; \frac{2 π}{3} + 2 k π; \frac{4 π}{3} + 2 k π}

⋃_{k \in Z} {k π; \frac{5 π}{6} + k π; \frac{7 π}{6} + k π}

⋃_{k \in Z} {k π; \frac{5 π}{6} + 2 k π; \frac{7 π}{6} + 2 k π}

1003086102

Level:

How many solutions does the equation

cotg (2 x - \frac{π}{4}) = \frac{1}{\sqrt{3}}

have in the interval

[0; 2 π]

4

8

2

0

1003086101

Level:

Which of the following equations has exactly four solutions in the interval

[0; π]

tg 4 x = 2

tg 2 x = 4

tg \frac{x}{4} = 2

tg \frac{x}{4} = 4

1003085810

Level:

Let

x \in (\frac{π}{2}; π]

. Which of the following statements is true?

\sin x \geq tg x

\sin x > tg x

\sin x < tg x

\sin x \leq tg x

1003085809

Level:

Which of the following inequalities has no solution for

x \in R

99 \cos x > 100

\cos^{2} x - \sin^{2} x \geq 1

\sin | x | < 0

\sin 2 x \leq 2

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Trigonometric equations and inequalities

1003086108

1003086107

1003086106

1003086105

1003086104

1003086103

1003086102

1003086101

1003085810

1003085809

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