Trigonometric equations and inequalities

1003085601

Level:

The solution set of the equation

\sin x = - 0.5

for

x \in [0; 2 π]

is:

{\frac{7 π}{6}; \frac{11 π}{6}}

{\frac{7 π}{6}}

{\frac{11 π}{6}}

{\frac{5 π}{6}; \frac{7 π}{6}}

1003085602

Level:

The solution set of the equation

tg x = - \sqrt{3}

for

x \in (0; π)

is:

{\frac{2 π}{3}}

{- \frac{2 π}{3}}

{\frac{π}{3}}

{\frac{5 π}{3}}

1003085603

Level:

How many solutions does the equation

\cos^{2} x = 0.25

have for

0 \leq x \leq 2 π

4

solutions

1

solution

2

solutions

3

solutions

1003085604

Level:

How many solutions does the equation

{tg}^{2} x = \frac{1}{3}

have for

0 \leq x \leq π

2

solutions

1

solution

4

solutions

3

solutions

1003085605

Level:

Find the set of all

x \in R

for which

\cos (\frac{π}{4} - x) = 1

{\frac{π}{4} + 2 k π : k \in Z}

{\frac{π}{2} + 2 k π : k \in Z}

{\frac{π}{4} + k π : k \in Z}

{\frac{π}{2} + k π : k \in Z}

1003085606

Level:

Find the set of all

x \in R

for which

\sin (\frac{π}{6} + x) = - 0.5

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

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

⋃_{k \in Z} {\frac{5 π}{3} + 2 k π}

⋃_{k \in Z} {\frac{7 π}{6} + 2 k π; \frac{11 π}{6} + 2 k π}

1003085607

Level:

Solve the equation

\sin (4 x - π) = 0

for

x \in R

x = \frac{k π}{4}, k \in Z

x = \frac{π}{4} + \frac{k π}{2}, k \in Z

x = \frac{k π}{2}, k \in Z

x = \frac{π}{2} + \frac{k π}{2}, k \in Z

1003085608

Level:

Find the set of all

x \in R

satisfying the equation

\cos (2 x - π) = - 1

{k π : k \in Z}

{\frac{π}{2} + 2 k π : k \in Z}

{2 k π : k \in Z}

{\frac{3 π}{2} + 2 k π : k \in Z}

1003085609

Level:

Find the set of all

x \in R

satisfying the equation

tg (3 x - π) = 1

{\frac{5 π}{12} + \frac{k π}{3} : k \in Z}

{\frac{5 π}{12} + k π : k \in Z}

{\frac{5 π}{4} + k π : k \in Z}

{\frac{5 π}{4} + \frac{k π}{3} : k \in Z}

1003085610

Level:

The solution set of the equation

cotg (2 x - π) = 1

for

x \in R

is:

{\frac{5 π}{8} + \frac{k π}{2} : k \in Z}

{\frac{5 π}{4} + k π : k \in Z}

{\frac{5 π}{8} + k π : k \in Z}

{\frac{5 π}{4} + \frac{k π}{2} : k \in Z}

Trigonometric equations and inequalities

1003085601

1003085602

1003085603

1003085604

1003085605

1003085606

1003085607

1003085608

1003085609

1003085610

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