What Is the Cosine Function?
The cosine function (cos) is a core trigonometric function. In a right triangle it is the ratio of the side adjacent to an angle to the hypotenuse. This calculator computes cos(x) for any angle you enter in degrees or radians, and shows the exact value for special angles.
cos(θ) = adjacent / hypotenuse. On the unit circle, cos(θ) equals the x-coordinate of the point at angle θ.Key Properties
Bounded Range
Unit Circle
Periodic
How to Use the Cos Calculator
Enter the Angle
Type your angle value in the input field. You can enter whole numbers, decimals, or π notation such as π/3, π/6, or an expression like 2π/3.
Choose DEG or RAD
Select DEG for degrees (the default) or RAD for radians. The input unit and placeholder update to match your choice.
Read the Result Instantly
The result updates automatically as you type — no submit button needed. The primary cos(x) value appears immediately.
View Exact & Related Values
For special angles, an exact value like √3/2 is shown. The secant (sec = 1/cos) appears as a related value, and a special-angles table can be expanded for reference.
Calculator Features
Degrees & Radians
Switch between DEG and RAD with one click, including support for π notation like π/3, π/6 and expressions such as 2π/3.
Exact Special Angles
Shows exact values such as 1/2, √2/2 and √3/2 for common angles instead of long decimals.
Related Secant
Displays the secant (sec = 1/cos) alongside the cosine result for quick reference.
Real-Time Calculation
Results update instantly as you type, with a special-angles table you can expand anytime.
Common Cosine Values
| Angle | cos value | Decimal |
|---|---|---|
| cos(0°) | 1 | 1.000 |
| cos(30°) | √3/2 | 0.866 |
| cos(45°) | √2/2 | 0.707 |
| cos(60°) | 1/2 | 0.500 |
| cos(90°) | 0 | 0.000 |
Frequently Asked Questions
What is the range of the cosine function?
The cosine function always returns values between −1 and 1, inclusive — that is, cos(x) ∈ [−1, 1]. No angle produces a cosine outside this range.
What is cos(0°) and cos(90°)?
cos(0°) = 1, the maximum value, reached when the angle points along the positive x-axis on the unit circle. cos(90°) = 0, where the point sits on the y-axis.
What is the difference between degrees and radians?
Both measure the same angle in different units: a full turn is 360° or 2π radians. cos(60°) and cos(π/3) give the same result (0.5). Use the DEG/RAD toggle to match your input, since the same number means a different angle in each mode.
What is the relationship between sin and cos?
They are cofunctions: sin(x) = cos(90° − x) and cos(x) = sin(90° − x). They also satisfy the Pythagorean identity sin²(x) + cos²(x) = 1.
What is the secant shown next to the result?
Secant is the reciprocal of cosine: sec(θ) = 1 / cos(θ). The calculator displays it alongside the cosine value. Where cos(θ) = 0 (such as 90°), the secant is undefined (∞).
How do I enter radians?
Click the RAD button, then enter the value. You can use π notation such as π/3, an expression like 2π/3, or a decimal like 1.0472.
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