Question

3sin^2α−7cos^2α , если cosα=−0,1

Answer 1

Ответ прикреплен ниже.

Answer 2

To find the value of the expression 3sin^2(α) - 7cos^2(α) when cos(α) = -0.1, we first need to determine the value of sin(α) using the given information.

Since cos(α) = -0.1, we can use the Pythagorean identity to find sin(α):

sin^2(α) + cos^2(α) = 1

sin^2(α) + (-0.1)^2 = 1

sin^2(α) + 0.01 = 1

sin^2(α) = 1 - 0.01

sin^2(α) = 0.99

sin(α) = ±√(0.99)

sin(α) ≈ ±0.994987

Now, we can find the value of the expression 3sin^2(α) - 7cos^2(α):

3sin^2(α) - 7cos^2(α) = 3(0.994987)^2 - 7(-0.1)^2 ≈ 3(0.989975) - 7(0.01) ≈ 2.969925 - 0.07 ≈ 2.899925

So, when cos(α) = -0.1, the value of the expression 3sin^2(α) - 7cos^2(α) is approximately 2.899925.