Question

Вычислить: √21cosa, если sina= √5/21, π/2 ≤ a ≤ π​

Answer 1

Ответ ответ ответ ответ ответ

Answer 2

To compute √(21) * cos(a), we first need to find the value of cos(a) given that sin(a) = √5/21 and π/2 ≤ a ≤ π.

We know that sin^2(a) + cos^2(a) = 1. Since we already know the value of sin(a), we can use this equation to find cos(a).

sin^2(a) + cos^2(a) = 1 (√5/21)^2 + cos^2(a) = 1 5/441 + cos^2(a) = 1 cos^2(a) = 1 - 5/441 cos^2(a) = (441 - 5) / 441 cos^2(a) = 436/441

Now, we take the square root of both sides to find the value of cos(a):

cos(a) = √(436/441) cos(a) = √436 / √441 cos(a) = √(4 * 109) / 21 cos(a) = (2 * √109) / 21

Now, we can compute the final value:

√(21) * cos(a) = √(21) * (2 * √109) / 21 √(21) * cos(a) = 2 * √(21 * 109) / 21 √(21) * cos(a) = 2 * √(2299) / 21

So, √(21) * cos(a) = 2 * √(2299) / 21.