Trigonometric equations and inequalities

1003086008

Level:

The solution set of the equation

tg x \cdot cotg x = 1

for

x \in R

is:

R ∖ {\frac{k π}{2} : k \in Z}

R

R ∖ {k π : k \in Z}

R ∖ {2 k π : k \in Z}

1003086007

Level:

The solution set of the equation

\sin^{4} x = 1 - \cos^{2} x

for

x \in [0^{\circ}; 360^{\circ}]

is:

{0^{\circ}; 90^{\circ}; 180^{\circ}; 270^{\circ}; 360^{\circ}}

{0^{\circ}; 180^{\circ}; 360^{\circ}}

{0^{\circ}; 90^{\circ}; 270^{\circ}; 360^{\circ}}

{90^{\circ}; 270^{\circ}}

1003086006

Level:

The sum of all

x

that are solutions of the equation

\sqrt{3} {cotg}^{2} x - 2 cotg x - \sqrt{3} = 0

on the interval

[0^{\circ}; 360^{\circ}]

is:

660^{\circ}

240^{\circ}

420^{\circ}

150^{\circ}

1003086005

Level:

The equation

3 {tg}^{2} x + 4 \sqrt{3} tg x + 3 = 0

has two solutions on the interval

[0^{\circ}; 180^{\circ}]

. The smaller one is:

120^{\circ}

150^{\circ}

30^{\circ}

60^{\circ}

1003086004

Level:

The arithmetic mean of all the solutions of the equation

\sin^{2} x - \cos^{2} x + \sin x = 0

on the interval

[0^{\circ}; 360^{\circ}]

is:

150^{\circ}

90^{\circ}

360^{\circ}

210^{\circ}

1003086003

Level:

The sum of all

x \in [0^{\circ}; 360^{\circ}]

satisfying the equation

\cos 2 x = \cos x

is:

720^{\circ}

360^{\circ}

480^{\circ}

120^{\circ}

1003086002

Level:

The equation

(\sin x + \cos x)^{2} = 1.5

has two solutions on the interval

(0^{\circ}; 90^{\circ})

. The larger one is:

75^{\circ}

15^{\circ}

30^{\circ}

65^{\circ}

1003086001

Level:

The arithmetic mean of all

x \in [0^{\circ}; 360^{\circ}]

satisfying the equation

\sin 2 x = \sin x

is:

180^{\circ}

240^{\circ}

360^{\circ}

270^{\circ}

1003086110

Level:

Which of the following intervals contains four solutions of the equation

\cos x = 0.5

[π; 5 π]

[- 2 π; π]

[- 4 π; - 2 π]

[5 π; 10 π]

1003086109

Level:

The solution set of the equation

tg x + cotg x = 2

for

x \in [- 2 π; 2 π]

is:

{- \frac{7 π}{4}; - \frac{3 π}{4}; \frac{π}{4}; \frac{5 π}{4}}

{- \frac{7 π}{4}; \frac{π}{4};}

{- \frac{5 π}{4}; - \frac{π}{4}; \frac{3 π}{4}; \frac{7 π}{4}}

{- \frac{3 π}{4}; \frac{π}{4}}

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Trigonometric equations and inequalities

1003086008

1003086007

1003086006

1003086005

1003086004

1003086003

1003086002

1003086001

1003086110

1003086109

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