Question

Arccos(-1)+arcsin0+arcsin(√3/2)+arctg(-1)

Answer 1

Ответ:

13π/12

Пошаговое объяснение:

arccos(-1)=π

arcsin0=0

arcsin(√3/2)= π/3

arctg(-1)= -π/4

arccos(-1)+arcsin0+arcsin(√3/2)+arctg(-1)= π+0+π/3-π/4=13π/12

Answer 2

To calculate the given expression, let's break it down step by step:

1. arccos(-1): The arccosine of -1 is equal to π radians or 180 degrees. Therefore, arccos(-1) = π.

2. arcsin(0): The arcsine of 0 is equal to 0 radians or 0 degrees. Therefore, arcsin(0) = 0.

3. arcsin(√3/2): The arcsine of √3/2 is equal to π/3 radians or 60 degrees. Therefore, arcsin(√3/2) = π/3.

4. arctg(-1): The arctangent of -1 is equal to -π/4 radians or -45 degrees. Therefore, arctg(-1) = -π/4.

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

π + 0 + π/3 + (-π/4)

Next, let's simplify the expression:

π + π/3 - π/4

To add the fractions with different denominators, we need to find a common denominator:

12π/12 + 4π/12 - 3π/12

Combining the fractions, we get:

(12π + 4π - 3π) / 12

Simplifying further:

13π / 12

Therefore, the value of the expression arccos(-1) + arcsin(0) + arcsin(√3/2) + arctg(-1) is 13π/12.