cos 45°
√2/2
The value of cos 45° is √2/2 or approximately 0.7071.
To understand why, we can use the unit circle, which is a circle with a radius of 1 unit. If we draw a line from the center of the circle to a point on its circumference, the angle formed by that line with the positive x-axis is the same as the angle in degrees.
For example, at 45°, the line intersects the circle at a point that is √2/2 units away from both the x and y axes. This can be verified using Pythagoras’ theorem.
The cosine function represents the x-coordinate of the point on the unit circle, so cos 45° is equal to √2/2.
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