Cosine Calculator
Enter an angle value and select its unit (degrees or radians) to calculate its cosine.
Calculation Result:
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The cosine function, often abbreviated as 'cos', is one of the fundamental trigonometric functions. In a right-angled triangle, the cosine of an angle is defined as the ratio of the length of the adjacent side to the length of the hypotenuse.
What is Cosine?
For a right-angled triangle with an angle θ (theta):
- Adjacent Side: The side next to the angle θ that is not the hypotenuse.
- Hypotenuse: The longest side of the right-angled triangle, opposite the right angle.
The formula for cosine is:
cos(θ) = Adjacent / Hypotenuse
Beyond right triangles, cosine can be understood in terms of the unit circle. For an angle θ measured counter-clockwise from the positive x-axis, the cosine of θ is the x-coordinate of the point where the terminal side of the angle intersects the unit circle.
Key Properties of the Cosine Function:
- Range: The value of cos(θ) always lies between -1 and 1, inclusive. That is, -1 ≤ cos(θ) ≤ 1.
- Periodicity: The cosine function is periodic with a period of 360 degrees or 2π radians. This means cos(θ) = cos(θ + 360°) = cos(θ + 2π).
- Even Function: Cosine is an even function, meaning cos(-θ) = cos(θ).
How to Use the Cosine Calculator
Our Cosine Calculator simplifies finding the cosine value for any given angle. Follow these steps:
- Enter Angle Value: Input the numerical value of the angle you wish to calculate the cosine for.
- Select Angle Unit: Choose whether your angle is in "Degrees" or "Radians" from the dropdown menu.
- Click "Calculate Cosine": The calculator will instantly display the cosine value, typically rounded to several decimal places for precision.
Examples of Cosine Values:
Here are some common angles and their cosine values:
- cos(0°) = 1 (or cos(0 radians) = 1)
- cos(30°) ≈ 0.866025 (or cos(π/6 radians) ≈ 0.866025)
- cos(45°) ≈ 0.707107 (or cos(π/4 radians) ≈ 0.707107)
- cos(60°) = 0.5 (or cos(π/3 radians) = 0.5)
- cos(90°) = 0 (or cos(π/2 radians) = 0)
- cos(180°) = -1 (or cos(π radians) = -1)
- cos(270°) = 0 (or cos(3π/2 radians) = 0)
- cos(360°) = 1 (or cos(2π radians) = 1)
Use the calculator above to verify these values or explore the cosine of other angles!