Question

-4 arcsin (-√2/2)+8 arccos (- √2/2)-15 arcctg √3/3=​

Answer 1

Ответ:

2π.

Пошаговое объяснение:

-4•arcsin (-√2/2) + 8 arccos (- √2/2) - 15 arcctg √3/3 = + 4•arcsin (√2/2) + 8•(π - arccos (√2/2) -15• arcctg (√3/3) = 4•π/4 + 8•(π - π/4) - 15•π/3 = π + 8•3π/4 - 5π = π + 6π - 5π = 2π.

Answer 2

To find the value of the expression:

-4 arcsin(-√2/2) + 8 arccos(-√2/2) - 15 arcctg(√3/3)

First, we need to evaluate each of the trigonometric functions for the given values:

1. arcsin(-√2/2): The arcsin function gives an angle whose sine is equal to the argument. In this case, we are looking for an angle whose sine is -√2/2. This angle is -π/4 (or -45 degrees).

2. arccos(-√2/2): The arccos function gives an angle whose cosine is equal to the argument. In this case, we are looking for an angle whose cosine is -√2/2. This angle is also -π/4 (or -45 degrees).

3. arcctg(√3/3): The arcctg (arctan) function gives an angle whose tangent is equal to the argument. In this case, we are looking for an angle whose tangent is √3/3. This angle is π/6 (or 30 degrees).

Now, substitute these values into the original expression:

-4(-π/4) + 8(-π/4) - 15(π/6)

Simplify each term:

-π + (-2π) - (5/2)π

Now, add the terms together:

-π - 2π - (5/2)π = -π(1 + 2 + 5/2)

Combine the constants:

-π(5/2 + 4/2 + 5/2) = -π(9/2)

Now, multiply:

-9π/2

So, the value of the expression is -9π/2, which is approximately equal to -14.13716.