Question

Найти 2√2cos, если sin=−1/3,∈(;3/2)

Answer 1

Твой ответ 0,4713965431453

Answer 2

Since we know that $\sin(x)=-\frac{1}{3}$, we can use the Pythagorean identity to find $\cos(x)$:

$\cos(x) = \pm\sqrt{1-\sin^2(x)} = \pm\sqrt{1-\left(-\frac{1}{3}\right)^2} = \pm\frac{2\sqrt{2}}{3}$

To determine the sign of $\cos(x)$, we need to know which quadrant $x$ is in. Since $\sin(x)$ is negative and $\cos(x)$ is either positive or negative, we know that $x$ is in the third quadrant.

In the third quadrant, $\cos(x)$ is negative, so we choose the negative sign:

$\cos(x) = -\frac{2\sqrt{2}}{3}$

Now we can use the identity $\sin(2x) = 2\sin(x)\cos(x)$ to find $2\sqrt{2}\cos(x)$:

$2\sqrt{2}\cos(x) = 2\sqrt{2}\left(-\frac{2\sqrt{2}}{3}\right) = -\frac{8}{3}$

Therefore, $2\sqrt{2}\cos(x) = -\frac{8}{3}$.