Question

Вычеслите 2аrcsin 1 +arccos(-√2\2)-3arctg (-1)

Answer 1

2*pi/2+3pi/4-3(-pi/4)=pi(1+3/4+3/4)=2.5pi

Answer 2

To compute the expression 2arcsin(1) + arccos(-√2/2) - 3arctg(-1), we'll start by evaluating each individual trigonometric function and then perform the necessary arithmetic operations.

1. arcsin(1): The arcsin function gives the angle whose sine is equal to the given value. Since sin(π/2) = 1, we have: arcsin(1) = π/2

2. arccos(-√2/2): The arccos function gives the angle whose cosine is equal to the given value. Since cos(π/4) = √2/2, we have: arccos(-√2/2) = π/4

3. arctg(-1): The arctg (or arctan) function gives the angle whose tangent is equal to the given value. Since tan(-π/4) = -1, we have: arctg(-1) = -π/4

Now, substitute these values back into the original expression:

2arcsin(1) + arccos(-√2/2) - 3arctg(-1) = 2(π/2) + π/4 - 3(-π/4)

Now, perform the arithmetic:

= π + π/4 + 3π/4 = π + 4π/4 = π + π = 2π

So, the final result is 2π.