Understanding the Value of cos(π/4) | Evaluating the Cosine Function at 45 Degrees

cos(π/4)

The expression cos(π/4) refers to the cosine function evaluated at the angle π/4, which is equivalent to 45 degrees

The expression cos(π/4) refers to the cosine function evaluated at the angle π/4, which is equivalent to 45 degrees.

To find the value of cos(π/4), we can use the unit circle or the special triangles.

On the unit circle, we draw a circle with a radius of one unit centered at the origin of a coordinate system. The angle π/4 is measured counterclockwise from the positive x-axis. At this angle, the terminal side of the angle intersects the unit circle at a point (x, y). Since the cosine function is defined as the x-coordinate of the point on the unit circle, we can conclude that cos(π/4) is equal to the x-coordinate of this point. In this case, we know that cos(π/4) = x.

Using the Pythagorean theorem, we can find the values of x and y for this point. The hypotenuse of the right triangle formed by the angle π/4 is the radius of the unit circle, which is 1. The legs of the triangle are equal in length, and by dividing the triangle into two 45-45-90 triangles, we know that each leg has a length of 1/√2.

So, cos(π/4) = x = 1/√2 ≈ 0.7071.

Therefore, cos(π/4) is approximately equal to 0.7071.

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