Základní goniometrické nerovnice III

Napsal uživatel michaela.bailova dne Pá, 12/13/2024 - 10:46.

Project ID:

7100020188

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Question:

Přiřaď ke každé goniometrické nerovnici množinu všech jejích řešení.

Question 1:

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

Answer 1:

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

Question 2:

tg x > 1

Answer 2:

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

Question 3:

cotg x < - 1

Answer 3:

⋃_{k \in Z} (\frac{3 π}{4} + k π, π + k π)

Question 4:

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

Answer 4:

⋃_{k \in Z} (\frac{5 π}{4} + 2 k π, \frac{7 π}{4} + 2 k π)

Question 5:

tg x < \sqrt{3}

Answer 5:

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

Question 6:

cotg x > 0

Answer 6:

⋃_{k \in Z} (0 + k π, \frac{π}{2} + k π)

Question 7:

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

Answer 7:

⋃_{k \in Z} (\frac{7 π}{6} + 2 k π, \frac{11 π}{6} + 2 k π)

Question 8:

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

Answer 8:

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

Question 9:

\sin x < \frac{\sqrt{3}}{2}

Answer 9:

⋃_{k \in Z} (- \frac{4 π}{3} + 2 k π, \frac{π}{3} + 2 k π)

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