Question

Найти cos alfa если sin alfa=-0,28 и alfa(π,3π/2)​

Answer 1

Ответ:

-24/25

Объяснение:

sinα= -0.28;   α∈(π;  3π/2)    III координат. оси

cos²α+sin²α=1

cos²α=1-sin²α=1-(-0.28)²=1-(28/100)²=1-(7/25)²=1-49/625=576/625

cos²α=576/625

cosα=±24/25

α∈(π;  3π/2)

cosα= -24/25

Answer 2

To find the value of cos(α) given that sin(α) = -0.28 and α is in the interval (π, 3π/2), we can use the Pythagorean identity for trigonometric functions.

Since sin(α) = -0.28, we can determine the value of cos(α) using the Pythagorean identity:

cos^2(α) = 1 - sin^2(α)

Substituting the value of sin(α) into the equation:

cos^2(α) = 1 - (-0.28)^2 cos^2(α) = 1 - 0.0784 cos^2(α) = 0.9216

Taking the square root of both sides:

cos(α) = ± √0.9216

Since α is in the interval (π, 3π/2), cos(α) is negative. Therefore:

cos(α) = -√0.9216

Calculating the square root:

cos(α) ≈ -0.9603

So, cos(α) is approximately -0.9603.