What is cos(45 degrees)?

cos(45 degrees) equals √2/2 or approximately 0.7071. To understand why that's the case, we can consider a right triangle where the two non-hypotenuse sides are equal, which would correspond to a 45-degree angle. In such a triangle, the cosine of 45 degrees is the ratio of the length of the adjacent side over the length of the hypotenuse. Since the sides are equal and the triangle is right-angled, by the Pythagorean theorem, we know that each side is of length 1 and the hypotenuse is of length √2. Therefore, cos(45°) = 1/√2, which simplifies to √2/2.

Extra: Cosine is a trigonometric function that essentially gives a ratio of two sides of a right-angled triangle; specifically, the length of the adjacent side over the hypotenuse. The concept of trigonometry deals with the relationships between the angles and sides of triangles, particularly right-angled triangles. Each trigonometric function—sine (sin), cosine (cos), and tangent (tan)—provides a different ratio, and these functions are fundamental in physics, engineering, and many fields that involve geometry or periodic phenomena. For an angle of 45 degrees, because it's half of 90 degrees, the right triangle splits into two identical right-angled isosceles triangles, making the calculations for the trigonometric functions particularly symmetrical and resulting in the nice sqrt(2)/2 value for cosine.