Question

Cos(5π/2+α),если sinα=0,5​

Answer 1

$Sin\alpha=0,5\\\\Cos(\frac{5\pi }{2}+\alpha)=Cos[2\pi+(\frac{\pi }{2}+\alpha)]=Cos(\frac{\pi }{2} +\alpha)=-Sin\alpha=-0,5$

Answer 2

To find the value of $\cos\left(\frac{5\pi}{2} + \alpha\right)$ given $\sin(\alpha) = 0.5$, we can use the following trigonometric identity:

$\cos(\theta) = \pm \sqrt{1 - \sin^2(\theta)}$

Since $\sin(\alpha) = 0.5$ and $\alpha$ is in the first or second quadrant (where $\sin(\alpha)$ is positive), we can take the positive square root.

$\cos(\alpha) = \sqrt{1 - \sin^2(\alpha)} = \sqrt{1 - 0.5^2} = \sqrt{1 - 0.25} = \sqrt{0.75}$

Now, to find $\cos\left(\frac{5\pi}{2} + \alpha\right)$, we know that $\frac{5\pi}{2}$ is in the third quadrant, where cosine is negative. So,

$\cos\left(\frac{5\pi}{2} + \alpha\right) = -\cos(\alpha) = -\sqrt{0.75}$

Therefore, $\cos\left(\frac{5\pi}{2} + \alpha\right) = -\sqrt{0.75}$.