Cosine of 60 Degrees | Definition, Calculation, and Example

cos 60°

The cosine of 60 degrees, denoted as cos(60°), is a trigonometric function that calculates the ratio of the length of the adjacent side to the length of the hypotenuse in a right triangle

The cosine of 60 degrees, denoted as cos(60°), is a trigonometric function that calculates the ratio of the length of the adjacent side to the length of the hypotenuse in a right triangle. In a right triangle, the adjacent side is the side that is next to the angle of interest (in this case, the 60-degree angle) and the hypotenuse is the longest side, which is opposite the right angle.

To find the cosine of 60 degrees, we can imagine a right triangle in which the angle of interest is 60 degrees. Let’s assume the adjacent side has a length of 1 unit and the hypotenuse has a length of 1 unit.

Using the Pythagorean theorem (a^2 + b^2 = c^2), we can find the length of the opposite side of the triangle. Let’s call it ‘b’.
1^2 + b^2 = 1^2
1 + b^2 = 1
b^2 = 1 – 1
b^2 = 0
b = 0

Now we have the lengths of all three sides of the right triangle: adjacent side = 1 unit, opposite side = 0 units, and hypotenuse = 1 unit.

The cosine of an angle is defined as the ratio of the adjacent side to the hypotenuse. So, in this case, cos(60°) = adjacent side / hypotenuse = 1 / 1 = 1.

Therefore, the cosine of 60 degrees is equal to 1.

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