To evaluate \(\cos 315^\circ\), we can use properties of the unit circle and trigonometric angles.
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Reference Angle: The angle \(315^\circ\) is in the fourth quadrant. The reference angle can be found by subtracting \(315^\circ\) from \(360^\circ\):
\[ 360^\circ - 315^\circ = 45^\circ \]
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Cosine in the Fourth Quadrant: In the fourth quadrant, the cosine function is positive.
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Value of Cosine at the Reference Angle: The cosine of the reference angle \(45^\circ\) is:
\[ \cos 45^\circ = \frac{\sqrt{2}}{2} \]
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Conclusion for \(\cos 315^\circ\): Since \(\cos 315^\circ\) uses the reference angle \(45^\circ\) and is positive in the fourth quadrant, we have:
\[ \cos 315^\circ = \cos 45^\circ = \frac{\sqrt{2}}{2} \]
Thus, the value of \(\cos 315^\circ\) is \(\frac{\sqrt{2}}{2}\).