Question

Arccos(-1/2)-arcsin(-1) решение?

Answer 1

Arccos(-1/2)-arcsin(-1)= π +π/2 = 3π/2
( табличные значения)

Answer 2

To find the value of the expression Arccos(-1/2) - Arcsin(-1), we'll start by evaluating each trigonometric function individually and then subtracting the results.

1. Arccos(-1/2): The arccosine function (Arccos) gives the angle whose cosine is the given value. In this case, we want to find the angle whose cosine is -1/2. We know that the cosine function is positive in the first and fourth quadrants.

In the first quadrant, there is an angle whose cosine is -1/2. This angle is approximately 120 degrees or (2π/3) radians.

In the fourth quadrant, the cosine function is also equal to -1/2, and the corresponding angle is 240 degrees or (4π/3) radians.

2. Arcsin(-1): The arcsine function (Arcsin) gives the angle whose sine is the given value. In this case, we want to find the angle whose sine is -1. The sine function is negative in the third and fourth quadrants.

In the third quadrant, there is an angle whose sine is -1, which is -90 degrees or -(π/2) radians.

3. Calculate the expression: Now, subtract Arcsin(-1) from Arccos(-1/2):

Arccos(-1/2) - Arcsin(-1) = (2π/3) - (-(π/2)) = (2π/3) + (π/2) = (4π + 3π)/(6) = 7π/6

So, the value of the expression Arccos(-1/2) - Arcsin(-1) is 7π/6 radians (approximately 330 degrees).