What is cosine
The cosine of an angle in a right triangle is the ratio of the side adjacent to the angle to the hypotenuse: cos(θ) = adjacent ÷ hypotenuse. Values range from −1 to 1. For example, cos(60°) = 0.5 and cos(0°) = 1.
The right-triangle picture only covers angles between 0° and 90°. For larger or negative angles, cosine is defined on the unit circle: place the angle at the origin, and cos(θ) is the x-coordinate of the point where the terminal side meets a circle of radius 1. That definition reproduces the triangle ratio in the first quadrant and extends smoothly to every real angle, which is why cosine is negative between 90° and 270°. If your angle is in degrees and the tool you are using expects radians, convert it with the degrees to radians calculator.
How to use this calculator
Enter the angle in degrees and read cos(θ) rounded to four decimals. To recover the angle from a cosine value, use the arccosine calculator.
Negative angles are accepted and give the same result as their positive counterparts, since cos(−θ) = cos(θ). Angles beyond 360° wrap around: cos(390°) equals cos(30°), because cosine repeats every 360 degrees. Values are rounded to four decimal places, so a result shown as 0 for 90° is exact, while long decimals such as cos(45°) ≈ 0.7071 are truncated for readability.
Cosine and sine
Cosine is the sine of the complementary angle: cos(θ) = sin(90° − θ). Together they satisfy the identity sin²θ + cos²θ = 1, the foundation of trigonometry.
That identity is just Pythagoras applied to a triangle with hypotenuse 1, where the two legs measure cos(θ) and sin(θ). It means you can always recover one function from the other up to sign, and it underpins the law of cosines, wave equations and phase calculations in physics and engineering.
Frequently asked questions
- What is cos(60°)?
- cos(60°) = 0.5, the ratio of the adjacent side to the hypotenuse for a 60-degree angle.
- What is the range of cosine?
- The cosine of any real angle is always between −1 and 1, inclusive.
- What is cos(0°)?
- cos(0°) = 1, the maximum value of the cosine function.
- How are sine and cosine related?
- cos(θ) = sin(90° − θ), and sin²θ + cos²θ = 1 for any angle θ.
- How do I enter an angle given in radians?
- Convert it to degrees first by multiplying by 180 ÷ π — this calculator expects degrees. For example, π/3 radians is 60 degrees, so entering 60 returns 0.5. Entering the radian value directly is the single most common source of wrong answers here.