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9000046510

Level:

Identify the optimal first step convenient to solve the following trigonometric equation. Do not consider the step which is possible but does not help to solve the equation.

2 \sin^{2} x - \sin x - 1 = 0

substitution

\sin x = z

substitution

\sin^{2} x = z

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

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

9000045709

Level:

Let

ω

be the angle between the solid diagonal of a box and the base of this box. Find the expression which allows to find

ω

tg ω = \frac{\sqrt{2}}{2}

\cos ω = \frac{\sqrt{2}}{2}

\sin ω = \frac{\sqrt{2}}{2}

cotg ω = \frac{\sqrt{2}}{2}

9000046407

Level:

Find the angle between the side of a cube and the cube’s space diagonal. Round the result to two decimal places.

{35.26}^{\circ}

45^{\circ}

{54.76}^{\circ}

9000046502

Level:

Identify the optimal first step convenient to solve the following trigonometric equation. Do not consider the step which is possible but does not help to solve the equation.

\cos 3 x = 0.5

substitution

3 x = z

substitution

\cos x = z

\cos^{3} x - \sin^{3} x = 0.5

\cos x = \frac{0.5}{3}

9000037406

Level:

Evaluate

{(\cos \frac{π}{4} + i \sin \frac{π}{4})}^{40}

1

1 + i

i

1 - i

9000037407

Level:

Evaluate

{(\cos \frac{π}{2} + i \sin \frac{π}{2})}^{13}

and find the algebraic form of the result.

i

1 + 2 i

1 - i

1

9000037410

Level:

Evaluate

{(1 - i)}^{3}

- 2 - 2 i

2 + 2 i

1 + i

i

9000037401

Level:

Evaluate

i^{50}

- 1

i

1

- i

9000037402

Level:

Evaluate

i^{7}

- i

- 1

i

1

9000037501

Level:

Find the absolute value of the following complex number.

3 + \sqrt{2} i

\sqrt{11}

\sqrt{13}

3

3 \sqrt{2}

A

9000046510

9000045709

9000046407

9000046502

9000037406

9000037407

9000037410

9000037401

9000037402

9000037501

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