Find the value of cos(405)°

To find the value of cos(405°), we need to understand how cosine functions behave with angles greater than 360°. In trigonometry, angles that exceed 360° represent more than one full rotation around a circle. The cosine function is periodic with a period of 360°, meaning it repeats its values every 360°. Therefore, to find the cosine of an angle greater than 360°, we can subtract multiples of 360° until the angle falls within the standard range of 0° to 360°.

For 405°, we subtract 360° (one full circle) to bring it within the standard range:

405°−360° = 45°

Now, we find the cosine of 45°. The cosine of 45° is a well-known value in trigonometry, which is ​​approximately 0.7071. Therefore, cos(405°) = cos(45°) = 1/√2

This property of cosine being a periodic function is crucial in trigonometry and is widely used in various fields, including physics, engineering, and computer science, to analyze wave patterns, circular motion, and oscillations.