Question

Arcsin (sin (25 пи / 8))

Answer 1

$arcsin(sin\frac{25\pi}{8}})=x\\ sin\frac{25\pi}{8}=sinx\\ x=\frac{25\pi}{8}$
Ответ $\frac{25\pi}{8}$  

Answer 2

To find the value of arcsin(sin(25π/8)), we can break down the problem step by step.

Step 1: Simplify the inside of the sine function. sin(25π/8) cannot be simplified further as it is an exact value.

Step 2: Apply the arcsin function to the simplified value. arcsin(sin(25π/8)) asks the question "What angle has a sine equal to sin(25π/8)?"

Step 3: Determine the principal value. The principal value of arcsin lies between -π/2 and π/2. To find the principal value, we need to determine the angle within this range that has the same sine value as sin(25π/8).

Step 4: Adjust the angle to lie within the principal value range. To adjust the angle, we can use the symmetry of the sine function. Since sin(x) = sin(π - x), we can subtract 2π from the given angle until it falls within the principal value range.

Let's calculate the value of arcsin(sin(25π/8)) step by step:

Step 1: Simplify the inside of the sine function. sin(25π/8) = sin(π/8 + 3π) = sin(π/8)

Step 2: Apply the arcsin function to the simplified value. arcsin(sin(π/8))

Step 3: Determine the principal value. Since π/8 falls within the range of -π/2 to π/2, the principal value of arcsin(sin(π/8)) is simply π/8.

Therefore, the value of arcsin(sin(25π/8)) is π/8.