Question

Arccos(-корень2/2)-arcsin(-1) объясните все пошагово пожалуйста

Answer 1

Arccos (-√2/2) = π - π/4 = (3π)/4 
arcsin(-1) = - (3π)/2 - это табличное значение, а минус не убрали, т.к. минус у синусов остаётся
Теперь подставляем данные значения в пример arccos(-корень2/2)-arcsin(-1):
(3π)/4 - (-(3π)/2) = (3π)/4 + (3π)/2 = (9π)/4

Answer 2

Calculation of arccos(-√2/2) - arcsin(-1)

To calculate the value of arccos(-√2/2) - arcsin(-1) step by step, we can use the trigonometric identities and properties. Let's break it down:

1. arccos(-√2/2): - The value of arccos(-√2/2) can be found using the trigonometric identity: arccos(x) = π/2 - arcsin(x). - Since the given value is -√2/2, we can find the value of arcsin(-√2/2) and then subtract it from π/2. - Using the trigonometric identity arcsin(x) = arcsin(-x), we can find the value of arcsin(√2/2). - From the search results, we can see that arcsin(√2/2) = π/4. - Therefore, arccos(-√2/2) = π/2 - π/4 = π/4.

2. arcsin(-1): - The value of arcsin(-1) represents the angle whose sine is -1. - From the search results, we can see that arcsin(-1) = -π/2.

3. Final calculation: - Now, we can substitute the values we found into the original expression: arccos(-√2/2) - arcsin(-1). - Substituting arccos(-√2/2) = π/4 and arcsin(-1) = -π/2, we get π/4 - (-π/2). - Simplifying the subtraction, we have π/4 + π/2. - Combining the fractions, we get (π + 2π) / 4 = 3π / 4.

Therefore, the value of arccos(-√2/2) - arcsin(-1) is 3π / 4.

Please let me know if you need any further clarification or have any additional questions!