Cosine Calculator — Calculate cos(x) and arccos
Calculate the cosine of any angle in degrees or radians, or find the inverse cosine (arccos). Shows all six trigonometric functions for the given angle. See also our Arctan Calculator and Trigonometry Calculator.
How to Calculate Cosine
- Select the mode: cosine (cos) or inverse cosine (arccos).
- For cos mode, enter the angle and select degrees or radians.
- For arccos mode, enter a value between -1 and 1.
- Click Calculate to see the result and all six trig functions.
Formula
cos(θ) = adjacent / hypotenuse (in a right triangle)
arccos(x) = θ, where cos(θ) = x
Domain of arccos: [-1, 1]
Range of arccos: [0°, 180°] or [0, π]
Conversion: radians = degrees × (π / 180)Example
Calculate cos(60°):
cos(60°) = 0.5
All trig functions at 60°:
sin(60°) = 0.866025, cos(60°) = 0.5, tan(60°) = 1.732051
csc(60°) = 1.154701, sec(60°) = 2.0, cot(60°) = 0.577350
Calculate arccos(0.5):
arccos(0.5) = 60° = 1.0472 radians
Cosine Reference Table
| Angle (°) | Radians | cos(θ) |
|---|---|---|
| 0° | 0 | 1.000000 |
| 30° | π/6 | 0.866025 |
| 45° | π/4 | 0.707107 |
| 60° | π/3 | 0.500000 |
| 90° | π/2 | 0.000000 |
| 120° | 2π/3 | -0.500000 |
| 180° | π | -1.000000 |
| 270° | 3π/2 | 0.000000 |
| 360° | 2π | 1.000000 |
Frequently Asked Questions
What is the cosine function?
Cosine is a trigonometric function that gives the ratio of the adjacent side to the hypotenuse in a right triangle. It is also the x-coordinate of a point on the unit circle.
What is the range of cosine?
The cosine function outputs values between -1 and 1 for all real inputs. cos(0°) = 1, cos(90°) = 0, cos(180°) = -1.
What is the difference between cos and arccos?
cos(θ) takes an angle and returns a ratio (-1 to 1). arccos(x) takes a ratio and returns the angle (0° to 180°). They are inverse functions.
Why does arccos only return 0 to 180 degrees?
Because cosine is not one-to-one over its full domain, arccos is restricted to [0°, 180°] to ensure a unique output for each input value.
How is cosine related to sine?
cos(θ) = sin(90° - θ). They are co-functions. Also, sin²(θ) + cos²(θ) = 1 (the Pythagorean identity).