Question

Arccos корень из 2/2 + arcsin корень из 3/2

Answer 1

Arccossgrt(2)/2+arcsinsgrt(3)/2=pi/4+pi/3=7pi/12
 Ответ: 7pi/12.

Answer 2

To calculate the value of the expression:

arccos(√2/2) + arcsin(√3/2)

We'll start by finding the values of arccos(√2/2) and arcsin(√3/2) using trigonometric identities.

1. arccos(√2/2): This value represents the angle whose cosine is √2/2. In other words, we are looking for the angle θ such that cos(θ) = √2/2.

We know that cos(π/4) = √2/2, so θ = π/4.

2. arcsin(√3/2): This value represents the angle whose sine is √3/2. In other words, we are looking for the angle θ such that sin(θ) = √3/2.

We know that sin(π/3) = √3/2, so θ = π/3.

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

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

To add these two angles, we need to find a common denominator:

π/4 = (3π)/12 π/3 = (4π)/12

Now, we can add the fractions:

(3π)/12 + (4π)/12 = (3π + 4π)/12 = 7π/12

Therefore, the value of the expression is 7π/12.