Question

Вычислить 12cos(0,5arccos1/8)=

Answer 1

Пусть arccos(1/8) будет β

Найдем  косинус половинного угла

cos (β/2) = √((1 + cos β)/2) = √(((1 + (1/8)) / 2) = √(9 / (2· 8)) = 3/4 

12 * 3/4 = 9

Answer 2

To compute the expression 12cos(0.5arccos(1/8)), follow these steps:

Step 1: Find the value of arccos(1/8). Step 2: Divide the result from Step 1 by 2. Step 3: Take the cosine of the result from Step 2. Step 4: Multiply the result from Step 3 by 12.

Step 1: arccos(1/8) ≈ 1.4426 radians (rounded to four decimal places).

Step 2: 0.5 * 1.4426 ≈ 0.7213 radians (rounded to four decimal places).

Step 3: cos(0.7213) ≈ 0.7489 (rounded to four decimal places).

Step 4: 12 * 0.7489 ≈ 8.9868 (rounded to four decimal places).

So, the final result is approximately 8.9868.