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Cosine

 

 

Cosine

cos alpha α = a/c

α = angle alpha

a = side "a"

b = side "b"

c = side "c"

WHAT IS IT ?

The cosine of an angle (cos) is the ratio of the length of the adjacent side to the hypotenuse.

 

 

CALCULATION:

Enter the unit of measure you want to use, e.g., cm

Enter the adjacent side

Enter the hypotenuse

Enter the angle α in degrees

Enter the number of decimal places

EXAMPLE:

Let's assume we have a right triangle ABC, where ∠C=90o. Side a is adjacent to angle alpha, side b is opposite to angle alpha, and c is the hypotenuse (the longest side of the triangle).

The definition of the cosine of angle α is:

The cosine of an angle (cos) is the ratio of the length of the adjacent side to the hypotenuse.

For this example:

cos⁡ α=a/c

Example:

Assume the side lengths are:

  • a = 3
  • b = 4
  • c = 5
  1. Verify that the triangle is right-angled using the Pythagorean theorem:

a2 + b2 = c2

32 + 42 = 52

9 + 16 = 25

Since the equality holds, it is a right triangle.

  1. Calculate the cosine of angle α:
cos⁡α = a/c = 3/5 = 0.6

Result:

cos⁡α = 0.6

Thus, the cosine of angle α in this right triangle is 0.6.

 



 

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