Question

Arctg(-1) + 2arccos(-1/2)

Answer 1

Ответ: pi/4+2*2*pi/3=pi/4+4*pi/3=(1,5*pi+8*pi)/6=95*pi/60=19*pi/12.

Пошаговое объяснение:

Answer 2

Let's calculate the values of the trigonometric functions involved in the expression step by step:

1. arctan(-1): The arctan function gives us the angle whose tangent is a specified number. In this case, arctan(-1) represents the angle whose tangent is -1. This angle is -π/4 radians (or -45 degrees).

2. arccos(-1/2): The arccos function gives us the angle whose cosine is a specified number. In this case, arccos(-1/2) represents the angle whose cosine is -1/2. This angle is 2π/3 radians (or 120 degrees).

Now, we can substitute these values into your expression:

arctan(-1) + 2arccos(-1/2) = (-π/4) + 2(2π/3)

Now, let's calculate this expression:

(-π/4) + 2(2π/3) = -π/4 + 4π/3

To add these fractions, we need a common denominator, which is 12:

(-3π/12) + (16π/12) = (16π - 3π) / 12 = 13π/12

So, the value of the expression arctan(-1) + 2arccos(-1/2) is 13π/12 radians.