Understanding the Trigonometric Function Cosine 45 Degrees in a Right Triangle – A Comprehensive Explanation

cos 45°

0.707

cos 45° is a trigonometric function that refers to the ratio of the adjacent side of a right triangle to its hypotenuse when the angle between them is 45 degrees.

We know that a right triangle with an angle of 45 degrees has two sides of equal length because it is an isosceles right triangle. Therefore, we can represent the adjacent side and hypotenuse as x.

Using the Pythagorean theorem, we can find the length of the opposite side of the triangle:

opposite^2 = hypotenuse^2 – adjacent^2
opposite^2 = x^2 – x^2/2
opposite^2 = x^2/2
opposite = x/√2

Now we can write the equation for cos 45°:

cos 45° = adjacent/hypotenuse
cos 45° = x/x
cos 45° = 1

Therefore, cos 45° is equal to 1.

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