Question

Arccos (-√2/2) + arcsin (-0,5)

Answer 1

Отметьте пожалуйста лучшим решением и поставьте сердечко

Answer 2

Ответ:

Пошаговое объяснение:

=3П/4  +(-П/6)=9П/12  -2П/12=7П/12

Answer 3

To evaluate the expression arccos(-√2/2) + arcsin(-0.5), we can use the properties of trigonometric functions.

First, let's determine the values of arccos(-√2/2) and arcsin(-0.5).

arccos(-√2/2) represents the angle whose cosine is equal to -√2/2. Since -√2/2 is the cosine value for the angle π/4 (45 degrees) in the fourth quadrant, we have:

arccos(-√2/2) = π/4

arcsin(-0.5) represents the angle whose sine is equal to -0.5. Since -0.5 is the sine value for the angle -π/6 (-30 degrees) in the third quadrant, we have:

arcsin(-0.5) = -π/6

Now, we can substitute these values into the original expression:

arccos(-√2/2) + arcsin(-0.5) = π/4 + (-π/6)

To simplify the expression, we need to find a common denominator for π/4 and -π/6. The common denominator is 12, so we can rewrite the expression as:

arccos(-√2/2) + arcsin(-0.5) = (3π/12) + (-2π/12)

Combining the terms, we get:

arccos(-√2/2) + arcsin(-0.5) = (3π - 2π)/12

Simplifying the numerator, we have:

arccos(-√2/2) + arcsin(-0.5) = π/12

Therefore, the value of the expression arccos(-√2/2) + arcsin(-0.5) is π/12 (approximately 0.2618).

Answer 4

To calculate the value of the expression arccos(-√2/2) + arcsin(-0.5), we can use the properties of inverse trigonometric functions and the values of trigonometric ratios.

Let's break it down step by step:

1. arccos(-√2/2): The value -√2/2 represents the cosine of an angle. We need to find the angle whose cosine is -√2/2. From the unit circle, we know that the cosine is negative in the second and third quadrants. In the second quadrant, the angle whose cosine is -√2/2 is 3π/4 (or 135 degrees).

2. arcsin(-0.5): The value -0.5 represents the sine of an angle. We need to find the angle whose sine is -0.5. From the unit circle, we know that the sine is negative in the third and fourth quadrants. In the third quadrant, the angle whose sine is -0.5 is -7π/6 (or -210 degrees).

Now, we can calculate the expression:

arccos(-√2/2) + arcsin(-0.5) = 3π/4 + (-7π/6)

To simplify this, we need to find a common denominator:

3π/4 + (-7π/6) = (9π/12) + (-14π/12)

Combining the terms:

= (9π - 14π) / 12 = -5π / 12

So, the value of the expression arccos(-√2/2) + arcsin(-0.5) is -5π/12.