Trigonometric equations and inequalities

1003085701

Level:

Find all

x

x \in R

, such that

{cotg}^{2} x = - cotg x

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

x \in ⋃_{k \in Z} {\frac{3 π}{4} + 2 k π}

x \in ⋃_{k \in Z} {\frac{3 π}{4} + k π}

x \in ⋃_{k \in Z} {\frac{π}{2} + k π}

1003085702

Level:

Solve

2 \sin^{2} x = \sqrt{2} \sin x

for

x

, where

x \in R

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

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

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

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

1003085703

Level:

The solution set of the equation

2 \sin (x - \frac{π}{6}) = 1

, where

x \in [0; π]

, is:

{\frac{π}{3}; π}

{\frac{π}{6}}

{\frac{π}{3}}

{\frac{π}{6}; \frac{π}{2}}

1003085704

Level:

The solution set of the equation

\cos (2 x - \frac{π}{3}) = - 0.5

, where

0 < x < 2 π

, is:

{\frac{π}{2}; \frac{3 π}{2}; \frac{5 π}{6}; \frac{11 π}{6}}

{\frac{π}{2}; \frac{3 π}{2}}

{\frac{5 π}{6}; \frac{11 π}{6}}

{\frac{3 π}{2}; \frac{5 π}{6}; \frac{11 π}{6}; π}

1003085705

Level:

Solving the equation

2 \sin (x + \frac{π}{4}) = \sqrt{3}

for

x

, where

x \in (0; π)

, you get:

x \in {\frac{π}{12}; \frac{5 π}{12}}

x \in {\frac{π}{12}}

x \in {\frac{3 π}{12}; \frac{5 π}{12}}

x \in {\frac{13 π}{12}; \frac{5 π}{12}}

1003085706

Level:

The sum of all

θ

, where

0^{\circ} < θ < 360^{\circ}

, satisfying the equation

\sin (θ + 10^{\circ}) = 0.5

is:

160^{\circ}

140^{\circ}

300^{\circ}

200^{\circ}

1003085707

Level:

Find

θ

between

0^{\circ}

and

360^{\circ}

such that

\sin (2 θ - 70^{\circ}) = - 1

170^{\circ}

85^{\circ}

340^{\circ}

255^{\circ}

1003085708

Level:

The arithmetic mean of all values of

θ

between

0^{\circ}

and

360^{\circ}

for which

\cos (θ - 20^{\circ}) = 0

is:

200^{\circ}

55^{\circ}

145^{\circ}

155^{\circ}

1003085709

Level:

The largest value of

θ

, where

0^{\circ} < θ < 360^{\circ}

, satisfying the equation

2 \cos (5 θ + 20^{\circ}) = - 1

is:

332^{\circ}

20^{\circ}

8^{\circ}

100^{\circ}

1003085710

Level:

The smallest value of

θ

, where

0^{\circ} < θ < 360^{\circ}

, satisfying the equation

2 \cos (2 θ + 10^{\circ}) = \sqrt{3}

is:

10^{\circ}

5^{\circ}

20^{\circ}

160^{\circ}

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Trigonometric equations and inequalities

1003085701

1003085702

1003085703

1003085704

1003085705

1003085706

1003085707

1003085708

1003085709

1003085710

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