To find the value of [tex]\(\cos 45^\circ\)[/tex], 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 [tex]\(\cos 45^\circ\)[/tex] corresponds to one of the standard angles. The x-coordinate (cosine) of the point on the unit circle corresponding to 45 degrees is [tex]\( \frac{\sqrt{2}}{2} \)[/tex].
3. Calculated value of cos 45°:
The exact value of [tex]\(\cos 45^\circ\)[/tex] is [tex]\(\frac{\sqrt{2}}{2}\)[/tex].
4. Numerical approximation:
When we express [tex]\(\frac{\sqrt{2}}{2}\)[/tex] in decimal form, it approximates to 0.7071067811865476.
Therefore, the value of [tex]\(\cos 45^\circ\)[/tex] is approximately 0.7071067811865476.
