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Cosine of an Angle(in Degrees)
[cos(θ)]
 cos()  =  1.000000 
 cos()  =  0.998630 
 cos()  =  0.994522 
 cos()  =  0.987688 
 cos()  =  0.978148 
 cos()  =  0.965926 
 cos()  =  0.951057 
 cos()  =  0.933580 
 cos()  =  0.913545 
 cos()  =  0.891007 
 cos()  =  0.866025 
 cos()  =  0.838671 
 cos()  =  0.809017 
 cos()  =  0.777146 
 cos()  =  0.743145 
 cos()  =  0.707107 
 cos()  =  0.669131 
 cos()  =  0.629320 
 cos()  =  0.587785 
 cos()  =  0.544639 
 cos()  =  0.500000 
 cos()  =  0.453990 
 cos()  =  0.406737 
 cos()  =  0.358368 
 cos()  =  0.309017 
 cos()  =  0.258819 
 cos()  =  0.207912 
 cos()  =  0.156434 
 cos()  =  0.104528 
 cos()  =  0.052336 
 cos()  =  0.000000 
 cos()  =  -0.052336 
 cos()  =  -0.104528 
 cos()  =  -0.156434 
 cos()  =  -0.207912 
 cos()  =  -0.258819 
 cos()  =  -0.309017 
 cos()  =  -0.358368 
 cos()  =  -0.406737 
 cos()  =  -0.453990 
 cos()  =  -0.500000 
 cos()  =  -0.544639 
 cos()  =  -0.587785 
 cos()  =  -0.629320 
 cos()  =  -0.669131 
 cos()  =  -0.707107 
 cos()  =  -0.743145 
 cos()  =  -0.777146 
 cos()  =  -0.809017 
 cos()  =  -0.838671 
 cos()  =  -0.866025 
 cos()  =  -0.891007 
 cos()  =  -0.913545 
 cos()  =  -0.933580 
 cos()  =  -0.951057 
 cos()  =  -0.965926 
 cos()  =  -0.978148 
 cos()  =  -0.987688 
 cos()  =  -0.994522 
 cos()  =  -0.998630 
 cos()  =  -1.000000 
 cos()  =  -0.998630 
 cos()  =  -0.994522 
 cos()  =  -0.987688 
 cos()  =  -0.978148 
 cos()  =  -0.965926 
 cos()  =  -0.951057 
 cos()  =  -0.933580 
 cos()  =  -0.913545 
 cos()  =  -0.891007 
 cos()  =  -0.866025 
 cos()  =  -0.838671 
 cos()  =  -0.809017 
 cos()  =  -0.777146 
 cos()  =  -0.743145 
 cos()  =  -0.707107 
 cos()  =  -0.669131 
 cos()  =  -0.629320 
 cos()  =  -0.587785 
 cos()  =  -0.544639 
 cos()  =  -0.500000 
 cos()  =  -0.453990 
 cos()  =  -0.406737 
 cos()  =  -0.358368 
 cos()  =  -0.309017 
 cos()  =  -0.258819 
 cos()  =  -0.207912 
 cos()  =  -0.156434 
 cos()  =  -0.104528 
 cos()  =  -0.052336 
 cos()  =  -0.000000 
 cos()  =  0.052336 
 cos()  =  0.104528 
 cos()  =  0.156434 
 cos()  =  0.207912 
 cos()  =  0.258819 
 cos()  =  0.309017 
 cos()  =  0.358368 
 cos()  =  0.406737 
 cos()  =  0.453990 

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What Is the Cosine of an Angle?

The cosine of an angle is a fundamental concept in trigonometry, and it relates to the angles and sides of a right triangle. Here's a beginner-friendly explanation:

What is a Right Triangle?

A right triangle is a triangle with one angle measuring 90 degrees. The longest side opposite this right angle is called the hypotenuse, and the other two sides are called the adjacent and opposite sides, depending on which angle you're focusing on.

Understanding Cosine

The cosine of an angle in a right triangle is a ratio that compares two sides of the triangle:

cos(θ) = (Adjacent Side) / (Hypotenuse)

Where:

  • θ is the angle you're interested in (not the 90° angle).
  • The Adjacent side is the side next to the angle θ.
  • The Hypotenuse is the longest side, opposite the right angle.

Example

Imagine a right triangle where the length of the adjacent side is 4 units, and the length of the hypotenuse is 5 units. To find the cosine of the angle θ, you'd use the formula:

cos(θ) = 4 / 5 = 0.8

This tells you that the cosine of the angle θ is 0.8, meaning the adjacent side is 80% the length of the hypotenuse.

Key Points to Remember

  • Cosine is a ratio that helps describe the relationship between an angle and the sides of a right triangle.
  • It's always between -1 and 1 for any angle.
  • It's useful in various applications, including finding unknown side lengths in triangles and working with wave functions in physics.

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