Trigonometric equations and inequalities

9000046606

Level:

Identify an inequality which is true for

x = \frac{3 π}{4}

cotg (- x) > 0

\sin 2 x > 0

tg x \cdot cotg x < \frac{\sqrt{2}}{2}

\cos^{2} x < 0

9000046607

Level:

Identify an inequality which is true for both

x = \frac{4 π}{3}

and

x = \frac{5 π}{3}

\sin x < \frac{1}{2}

tg x > 0

\cos x < 0

cotg x \leq - 1

9000046608

Level:

Identify an inequality which is true for both

x = \frac{π}{6}

and

x = - \frac{π}{6}

\cos x > 0

\sin x > \frac{1}{2}

| tg x | < \frac{1}{2}

cotg x \leq - 1

9000046609

Level:

Identify an inequality which is true for every

x

from the interval

(\frac{π}{4}; \frac{3 π}{4})

\sin x \geq \frac{\sqrt{2}}{2}

tg x > 1

\cos x > 0

cotg x \geq \frac{\sqrt{3}}{3}

9000046610

Level:

Identify an inequality which is true for every

x

from the interval

(\frac{5 π}{6}; \frac{3 π}{2})

\cos x < \frac{1}{2}

tg x < 0

\sin x \geq - \frac{\sqrt{2}}{2}

cotg x < 1

1003085901

Level:

The solution set of the inequality

\cos^{2} x \leq 0.25

for

x \in [0; 2 π]

is:

[\frac{π}{3}; \frac{2 π}{3}] \cup [\frac{4 π}{3}; \frac{5 π}{3}]

[\frac{π}{3}; \frac{5 π}{3}]

[0; \frac{2 π}{3}]

[0; \frac{5 π}{3}]

1003085902

Level:

The solution set of the inequality

\sin^{2} x \geq 0.75

for

x \in [0; 2 π]

is:

[\frac{π}{3}; \frac{2 π}{3}] \cup [\frac{4 π}{3}; \frac{5 π}{3}]

[\frac{π}{3}; \frac{5 π}{3}]

[0; \frac{2 π}{3}]

[0; \frac{5 π}{3}]

1003085905

Level:

The solution set of the inequality

| cotg x | \leq \sqrt{3}

for

x \in R

is:

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

⋃_{k \in Z} [\frac{π}{6} + k π; \frac{π}{2} + k π]

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

⋃_{k \in Z} [k π; (k + 1) π]

1003085906

Level:

The solution set of the inequality

\cos 3 x > \frac{\sqrt{3}}{2}

for

x \in (0^{\circ}; 180^{\circ})

is:

(0^{\circ}; 10^{\circ}) \cup (110^{\circ}; 130^{\circ})

(330^{\circ}; 360^{\circ})

(110^{\circ}; 120^{\circ})

(0^{\circ}; 30^{\circ})

1003085907

Level:

The solution set of the inequality

| \sin x | \geq 0.5

for

x \in [0; 2 π]

is:

[\frac{π}{6}; \frac{5 π}{6}] \cup [\frac{7 π}{6}; \frac{11 π}{6}]

[0; \frac{5 π}{6}] \cup [\frac{7 π}{6}; \frac{11 π}{6}]

[\frac{π}{6}; \frac{11 π}{6}]

[0; \frac{π}{6}] \cup [\frac{5 π}{6}; \frac{11 π}{6}]

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Trigonometric equations and inequalities

9000046606

9000046607

9000046608

9000046609

9000046610

1003085901

1003085902

1003085905

1003085906

1003085907

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