Trigonometric equations and inequalities

1003085801

Level:

The solution set of the inequality

\cos x > 0.5

for

x \in R

is:

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

⋃_{k \in Z} (- \frac{π}{3} + k π; \frac{π}{3} + k π)

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

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

1003085802

Level:

The solution set of the inequality

tg x \leq \frac{\sqrt{3}}{3}

for

x \in R

is:

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

⋃_{k \in Z} (\frac{π}{6} + k π; \frac{π}{3} + k π)

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

⋃_{k \in Z} (\frac{π}{6} + 2 k π; \frac{π}{3} + 2 k π)

1003085803

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; (k + 1) π)

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

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

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

1003085804

Level:

The solution set of the inequality

\sin x > \cos x

for

x \in R

is:

⋃_{k \in Z} (\frac{π}{4} + 2 k π; \frac{5 π}{4} + 2 k π)

⋃_{k \in Z} (\frac{π}{4} + k π; \frac{5 π}{4} + k π)

⋃_{k \in Z} (\frac{π}{3} + 2 k π; \frac{5 π}{3} + 2 k π)

⋃_{k \in Z} (\frac{π}{3} + k π; \frac{5 π}{3} + k π)

1003085805

Level:

The solution set of the inequality

2 \sin x \leq 3

for

x \in R

is:

R

\emptyset

[0; π]

[0; 2 π]

1003085806

Level:

The solution set of the inequality

tg x > 1

for

0 \leq x \leq π

is the interval:

(\frac{π}{4}; \frac{π}{2})

(0; \frac{π}{4})

(0; \frac{π}{2})

(\frac{π}{2}; π)

1003085807

Level:

For which

x \in (- \frac{π}{2}; \frac{π}{2})

is the inequality

tg 3 x < - 1

true?

x \in (- \frac{π}{2}; - \frac{5 π}{12}) \cup (- \frac{π}{6}; - \frac{π}{12}) \cup (\frac{π}{6}; \frac{π}{4})

x \in (- \frac{π}{6}; - \frac{π}{12}) \cup (\frac{π}{6}; \frac{π}{4})

x \in (- \frac{π}{2}; - \frac{5 π}{12}) \cup (- \frac{π}{6}; - \frac{π}{12})

x \in (- \frac{π}{6}; - \frac{π}{12}) \cup (\frac{π}{12}; \frac{π}{6}) \cup (\frac{π}{6}; \frac{π}{4})

1003085808

Level:

Which of the following inequalities has no solutions for

x \in R

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

100 \sin x > 1

\sin x \cdot \cos x \geq \frac{1}{2}

| \sin x | \geq 1

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

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

Trigonometric equations and inequalities

1003085801

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