Cosine Calculator

Category: Algebra II
- May 25, 2025
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Calculate the cosine of any angle. Also provides related trigonometric values and visualisations.

Angle Input

Display Options

About Cosine Function

The cosine is one of the fundamental trigonometric functions. For an angle θ in a right-angled triangle, the cosine equals the ratio of the adjacent side to the hypotenuse.

Key Properties
  • Domain: All real numbers
  • Range: [-1, 1]
  • Period: 360° or 2π radians
  • cos(0°) = 1
  • cos(90°) = 0
  • cos(180°) = -1
  • cos(360°) = 1
Important Identities
  • cos(-θ) = cos(θ) (cosine is an even function)
  • cos(θ + 2π) = cos(θ) (periodicity)
  • sin²(θ) + cos²(θ) = 1 (Pythagorean identity)
  • cos(α + β) = cos(α)cos(β) - sin(α)sin(β)
  • cos(α - β) = cos(α)cos(β) + sin(α)sin(β)

Understanding the Cosine Calculator

The Cosine Calculator is a handy tool for finding the cosine of any angle you input. It helps you grasp how this function works and what it means in trigonometry. This calculator not only gives you the cosine value but also provides additional trigonometric results like sine, tangent, and more.

How to Input Angles

When using the calculator, you can enter the angle in different units. Whether you prefer degrees, radians, or gradians, the tool allows you to choose your preferred measurement. You simply type your angle into the input box and select the unit that fits you best.

Customising Your Results

The calculator offers options to tailor your results. You can choose how many decimal places you want for your answers, with options ranging from two to ten. You can also decide if you want to see the calculation steps and all related trigonometric values displayed. This way, you can understand how the results were derived.

Visualising the Cosine Function

To help you better understand the cosine function, the calculator includes a visual representation using a unit circle. This illustration shows the relationship between angles and their cosine values, making it easier to see how the cosine corresponds to points on the circle.

Exploring Trigonometric Values

  • Sine: The sine value of the angle is also calculated, showing the opposite side to the hypotenuse ratio.
  • Tangent: You’ll get the tangent value, which relates to sine and cosine.
  • Secant: The calculator provides the secant, which is the reciprocal of cosine.
  • Cosecant: This value is the reciprocal of sine.
  • Cotangent: Finally, you receive the cotangent value, the reciprocal of tangent.

The Cosine Formula Explained

The formula for cosine states that it gives the ratio of the adjacent side to the hypotenuse in a right triangle. Mathematically, it’s expressed as:

cos(θ) = adjacent / hypotenuse
This formula helps you see why cosine is important in various applications, from Physics to engineering.

Key Properties of the Cosine Function

  • Domain: All real numbers
  • Range: From -1 to 1
  • Period: 360° or 2π radians
  • Special Values: cos(0°) = 1, cos(90°) = 0, cos(180°) = -1

The Importance of Cosine in Real Life

Cosine isn't just a theoretical concept; it has practical applications in real life. Engineers and architects use cosine to calculate angles and distances. In computer graphics, it helps in rendering images with correct angles. This makes understanding cosine essential for many practical fields.