Question

Вычислите: 49*cos(2arccos4/7)

Answer 1

Ответ:

Пошаговое объяснение:

cos2a=2cos²a-1; cos(arccosa))=a

49*(2cos²arccos(4/7)-1)=49(2(cos(arccos(4/7))²-1))=49(2(4/7)²-1))=49(2(4/7)²-1)

49(32/49-1)=49(-17/49)=-17

Answer 2

To compute the value of the expression 49 * cos(2 * arccos(4/7)), we can follow these steps:

Step 1: Find the value of arccos(4/7). Step 2: Compute the value of cos(2 * arccos(4/7)). Step 3: Multiply the result by 49.

Let's go through each step:

Step 1: Find the value of arccos(4/7). arccos(4/7) is the angle whose cosine is equal to 4/7. Using a calculator or trigonometric tables, we can find this value: arccos(4/7) ≈ 0.8873 radians (rounded to four decimal places).

Step 2: Compute the value of cos(2 * arccos(4/7)). cos(2 * arccos(4/7)) = cos(2 * 0.8873) cos(2 * 0.8873) = cos(1.7746)

Step 3: Multiply the result by 49. 49 * cos(1.7746) ≈ 49 * 0.1901 ≈ 9.3121

Therefore, the value of the expression 49 * cos(2 * arccos(4/7)) is approximately 9.3121 (rounded to four decimal places).