Cosine (Cos) Calculator
Compute the cosine of any angle in degrees with our free cosine calculator. Get cos(θ), sin(θ), tan(θ) plus an interactive cosine wave chart for students and professionals.
About This Calculator
The Cosine (Cos) Calculator computes the cosine of any angle in degrees using standard trigonometric formulas. Enter an angle and get instant results for cos(θ), sin(θ), and tan(θ) along with an interactive wave chart showing the cosine function from 0° to 360° with your angle highlighted.
Cosine is one of the six fundamental trigonometric functions. For a right triangle, cos(θ) = adjacent/hypotenuse. On the unit circle, it represents the x-coordinate of a point at angle θ from the positive x-axis. The cosine function is even (cos(-θ) = cos(θ)), periodic with period 360° (2π radians), and has a range of -1 to 1.
Common cosine values include cos(0°) = 1, cos(30°) = √3/2 ≈ 0.8660, cos(45°) = √2/2 ≈ 0.7071, cos(60°) = 1/2, cos(90°) = 0, cos(180°) = -1, and cos(360°) = 1. The cosine function reaches its maximum value of 1 at 0° and 360°, and its minimum value of -1 at 180°.
Cosine is related to sine through the cofunction identity cos(θ) = sin(90° - θ), and the Pythagorean identity cos²(θ) + sin²(θ) = 1. The double-angle formula gives cos(2θ) = cos²(θ) - sin²(θ) = 2cos²(θ) - 1 = 1 - 2sin²(θ).
Cosine has numerous applications in physics (waves, oscillations, periodic motion), engineering (signal processing, AC circuits), computer graphics (rotation matrices, lighting calculations), navigation, and surveying. The Law of Cosines c² = a² + b² - 2ab·cos(C) is used to solve any triangle when two sides and the included angle are known.
How to Use
Enter any angle in degrees (positive, negative, or greater than 360°) and click Calculate. The result panel shows cos(θ), sin(θ), tan(θ), and the input angle. The wave chart displays the full cosine function from 0° to 360° with your calculated point marked in red. The chart is interactive — hover to see values at any point.
Frequently Asked Questions
What is cosine and how is it calculated?
Cosine (cos) is a trigonometric function defined as the ratio of the adjacent side to the hypotenuse in a right triangle. For an angle θ in degrees, cos(θ) = adjacent/hypotenuse. It is also defined on the unit circle as the x-coordinate of a point at angle θ from the positive x-axis.
What is the range and period of the cosine function?
The cosine function has a range of -1 to 1 and a period of 360 degrees (2π radians). It is an even function, meaning cos(-θ) = cos(θ). The maximum value of 1 occurs at 0° and 360°, and the minimum value of -1 occurs at 180°.
What are the exact cosine values for common angles?
cos(0°) = 1, cos(30°) = √3/2 ≈ 0.8660, cos(45°) = √2/2 ≈ 0.7071, cos(60°) = 1/2 = 0.5, cos(90°) = 0, cos(120°) = -1/2 = -0.5, cos(180°) = -1, cos(270°) = 0, cos(360°) = 1.
What is the relationship between cosine and sine?
Cosine and sine are related by the identity cos(θ) = sin(90° - θ). They are cofunctions of complementary angles. On the unit circle, cos(θ) represents the x-coordinate while sin(θ) represents the y-coordinate of the same point, and they satisfy cos²(θ) + sin²(θ) = 1.
Is this cosine calculator free to use?
Yes, it is completely free to use with no registration or hidden charges. You can calculate cosine values for any angle in degrees and view the interactive wave chart instantly.
Can I share my cosine calculation results?
Yes, the URL saves your angle input so you can bookmark or share the exact calculation with others. Simply copy the URL after calculating.
How accurate are the cosine results?
Results are computed using JavaScript's built-in Math.cos function which provides IEEE 754 double-precision floating point accuracy. Results are displayed rounded to 6 decimal places for readability.
Can I compute cosine for angles greater than 360 degrees?
Yes, the cosine function is periodic with a period of 360 degrees, so cos(θ + 360°k) = cos(θ) for any integer k. The calculator accepts any angle value and computes the correct cosine.