Question

4arccos(-√2/2)-3arccos1+2arcsin1/2-arctg√3/3​

Answer 1

Ответ:

19π/6.

Пошаговое объяснение:

4arccos(-√2/2) - 3arccos1 + 2arcsin1/2 - arctg√3/3 = 4•(π - arccos√2/2) - 3•0 + 2•π/6 - π/6 = 4•(π - π/4) - 0 + 2π/6 - π/6 = 3π + π/6 = 3 1/6•π (или 19π/6).

Answer 2

To simplify the expression, let's evaluate each term step by step:

1. 4arccos(-√2/2): The value of arccos(-√2/2) is π/4. Therefore, 4arccos(-√2/2) = 4 * (π/4) = π.

2. 3arccos1: The value of arccos1 is 0. Therefore, 3arccos1 = 3 * 0 = 0.

3. 2arcsin(1/2): The value of arcsin(1/2) is π/6. Therefore, 2arcsin(1/2) = 2 * (π/6) = π/3.

4. arctg(√3/3): The value of arctg(√3/3) is π/6. Therefore, arctg(√3/3) = π/6.

Now, let's substitute the values back into the original expression:

π - 0 + π/3 - π/6

Combining like terms, we have:

(π + π/3 - π/6)

To simplify further, we need to find a common denominator for π, π/3, and π/6, which is 6.

(6π/6 + 2π/6 - π/6)

Now, we can add the fractions:

(7π/6)

Therefore, the simplified expression is 7π/6.