Trigonometric equations and inequalities

2000006302

Level:

An inequality is solved graphically as shown in the picture. The solution is marked in red. Choose the corresponding inequality.

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

x \in [0; 2 π]

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

x \in [0; 2 π]

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

x \in [0; 2 π]

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

x \in [0; 2 π]

2000006303

Level:

An inequality is solved graphically as shown in the picture. The solution is marked in red. Choose the corresponding inequality.

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

x \in [0; 2 π]

\cos x \leq \frac{\sqrt{2}}{2}

x \in [0; 2 π]

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

x \in [0; 2 π]

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

x \in [0; 2 π]

2000006304

Level:

An inequality is solved graphically as shown in the picture. The solution is marked in red. Choose the corresponding inequality.

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

x \in [0; 2 π]

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

x \in [0; 2 π]

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

x \in [0; 2 π]

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

x \in [0; 2 π]

2000006601

Level:

An inequality is solved graphically as shown in the picture. The solution is marked in red. Choose the corresponding inequality.

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

x \in [0; π] ∖ {\frac{π}{2}}

tg x \geq \frac{\sqrt{3}}{2}

x \in [0; π] ∖ {\frac{π}{2}}

cotg x \geq \frac{\sqrt{3}}{2}

x \in [0; π] ∖ {\frac{π}{2}}

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

x \in [0; π] ∖ {\frac{π}{2}}

2000006602

Level:

An inequality is solved graphically as shown in the picture. The solution is marked in red. Choose the corresponding inequality.

tg x \leq - \sqrt{3}

x \in [- π; π] ∖ {- \frac{π}{2}; \frac{π}{2}}

tg x \geq - \sqrt{3}

x \in [- π; π] ∖ {- \frac{π}{2}; \frac{π}{2}}

cotg x \leq - \sqrt{3}

x \in [- π; π] ∖ {- \frac{π}{2}; \frac{π}{2}}

cotg x \geq - \sqrt{3}

x \in [- π; π] ∖ {- \frac{π}{2}; \frac{π}{2}}

2000006603

Level:

An inequality is solved graphically as shown in the picture. The solution is marked in red. Choose the corresponding inequality.

cotg x \leq 1

x \in (- π; π) ∖ {0}

cotg x \geq 1

x \in (- π; π) ∖ {0}

tg x \leq 1

x \in (- π; π) ∖ {0}

tg x \geq 1

x \in (- π; π) ∖ {0}

2000006604

Level:

An inequality is solved graphically as shown in the picture. The solution is marked in red. Choose the corresponding inequality.

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

x \in (- π; π) ∖ {0}

cotg x \geq \frac{1}{2}

x \in (- π; π) ∖ {0}

cotg x \geq \frac{\sqrt{3}}{2}

x \in (- π; π) ∖ {0}

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

x \in (- π; π) ∖ {0}

2010014901

Level:

The solution set of the inequality

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

for

x \in R

is:

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

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

⋃_{k \in Z} [- \frac{π}{4} + 2 k π; \frac{π}{4} + 2 k π]

⋃_{k \in Z} [- \frac{π}{4} + k π; \frac{π}{4} + k π]

2010014902

Level:

The solution set of the inequality

tg x > - \frac{\sqrt{3}}{3}

for

x \in R

is:

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

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

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

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

2010014903

Level:

The solution set of the inequality

\cos x < - \frac{\sqrt{3}}{2}

for

x \in R

is:

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

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

⋃_{k \in Z} (\frac{5 π}{6} + 2 k π; \frac{11 π}{6} + 2 k π)

⋃_{k \in Z} (- \frac{5 π}{6} + 2 k π; \frac{5 π}{6} + 2 k π)

Trigonometric equations and inequalities

2000006302

2000006303

2000006304

2000006601

2000006602

2000006603

2000006604

2010014901

2010014902

2010014903

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