To find the value of \(\(\cos 45^\circ\)\), we need to follow these steps:
1. Understand the angle:
We are given an angle of 45 degrees, which is a common angle in trigonometry.
2. Reference to unit circle or trigonometric values:
In trigonometry, it's well-known that \(\(\cos 45^\circ\)\) corresponds to one of the standard angles. The x-coordinate (cosine) of the point on the unit circle corresponding to 45 degrees is \(\( \frac{\sqrt{2}}{2} \)\).
3. Calculated value of cos 45°:
The exact value of \(\(\cos 45^\circ\)\) is \(\(\frac{\sqrt{2}}{2}\)\).
4. Numerical approximation:
When we express \(\(\frac{\sqrt{2}}{2}\)\) in decimal form, it approximates to 0.7071067811865476.
Therefore, the value of \(\(\cos 45^\circ\)\) is approximately 0.7071067811865476.
