Find cos(225^circ ) sqrt (2) (-1)/(sqrt (2)) (1)/(sqrt (3)) -(sqrt (2))/(2)

To find $\cos(225^{\circ})$, we can use the unit circle and the properties of the cosine function.<br /><br />The angle $225^{\circ}$ is in the third quadrant of the unit circle, where the cosine values are negative.<br /><br />We can use the reference angle $45^{\circ}$ to find the cosine value.<br /><br />The reference angle $45^{\circ}$ is the acute angle formed by the terminal side of $225^{\circ}$ and the positive x-axis.<br /><br />The cosine of an angle in the third quadrant is the negative of the cosine of its reference angle.<br /><br />So, $\cos(225^{\circ}) = -\cos(45^{\circ})$<br /><br />The cosine of $45^{\circ}$ is $\frac{1}{\sqrt{2}}$.<br /><br />Therefore, $\cos(225^{\circ}) = -\frac{1}{\sqrt{2}}$<br /><br />The correct answer is $\frac{-1}{\sqrt{2}}$.