Trigonometric equations and inequalities

9000086701

Level:

Identify the optimal substitution which simplifies the following equation as much as possible.

\sin (3 x + \frac{π}{6}) = 0

(3 x + \frac{π}{6}) = t

3 x = t

\sin 3 x = \frac{π}{6} t

\sin 3 x = t

9000086702

Level:

Identify the optimal substitution which simplifies the following equation as much as possible.

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

\sin 2 x = t

x = t

Equation is not convenient for a substitution.

\sin x = t

9000086703

Level:

Identify the optimal substitution which simplifies the following equation as much as possible.

5 cotg (30^{\circ} - 4 y) = 0

30^{\circ} - 4 y = t

cotg (30^{\circ} - 4 y) = t

cotg (30^{\circ} - 4 y) = 0

4 y = 0

9000086704

Level:

Identify the optimal substitution which simplifies the following equation as much as possible.

{tg}^{2} v - {cotg}^{- 1} v = 2

tg v = t

v^{- 1} = t

cotg v = t

Equation is not convenient for a substitution.

9000086705

Level:

Identify the optimal substitution which simplifies the following equation as much as possible.

2 \cos (3 x + 33^{\circ}) = - \sqrt{2}

3 x + 33^{\circ} = t

\sin 3 x = t

3 x = t

3 x + 33^{\circ} = - \sqrt{2}

9000086706

Level:

Identify the equation which arises from the following equation using an optimal substitution.

2 \cos^{2} x - 7 \cos x + 3 = 0

2 t^{2} - 7 t + 3 = 0

2 t^{2} = \frac{3}{7}

\cos t = 0

7 \cos t = 3

9000086707

Level:

Identify the equation which arises from the following equation using an optimal substitution.

{tg}^{2} y - 2 tg y = 3

t^{2} - 2 t - 3 = 0

tg t = \frac{3}{2}

t^{2} = \frac{3}{2}

tg t = 3

9000086708

Level:

Identify the equation which arises from the following equation using an optimal substitution.

{tg}^{2} v - {cotg}^{- 1} v = 2

t^{2} - t - 2 = 0

Equation is not convenient for a substitution.

t^{2} + t = 0

tg t = 2

9000086709

Level:

Identify the equation which arises from the following equation using an optimal substitution.

6 \cos^{2} x + \sin x - 5 = 0

6 t^{2} - t = 1

6 t^{2} + t - 5 = 0

6 t = 5

Equation is not convenient for a substitution.

9000086710

Level:

Identify the equation which arises from the following equation using an optimal substitution.

2 tg x + 3 cotg x = 5

2 t^{2} - 5 t = - 3

2 t^{2} + 3 t - 5 = 0

2 t = \frac{3}{5}

2 t + 3 t = 5

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Trigonometric equations and inequalities

9000086701

9000086702

9000086703

9000086704

9000086705

9000086706

9000086707

9000086708

9000086709

9000086710

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