Sine, Cosine, and Tangent Calculator
Results:
Sine (sin):
Cosine (cos):
Tangent (tan):
Understanding Sine, Cosine, and Tangent
Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles. The three fundamental trigonometric ratios are sine, cosine, and tangent, often abbreviated as sin, cos, and tan. These functions are crucial in various fields, including physics, engineering, architecture, and computer graphics.
What are Sine, Cosine, and Tangent?
In a right-angled triangle, these ratios relate the angles to the lengths of its sides:
- Sine (sin): The ratio of the length of the side opposite the angle to the length of the hypotenuse.
sin(θ) = Opposite / Hypotenuse - Cosine (cos): The ratio of the length of the side adjacent to the angle to the length of the hypotenuse.
cos(θ) = Adjacent / Hypotenuse - Tangent (tan): The ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.
tan(θ) = Opposite / Adjacent = sin(θ) / cos(θ)
These definitions are for angles within a right triangle (0 to 90 degrees). For angles beyond this range, the unit circle provides a more general definition, where sine corresponds to the y-coordinate, cosine to the x-coordinate, and tangent to the ratio y/x of a point on the unit circle.
Degrees vs. Radians
Angles can be measured in two primary units: degrees and radians.
- Degrees: A full circle is divided into 360 degrees. This is the most common unit for everyday use and geometry.
- Radians: A radian is the angle subtended at the center of a circle by an arc that is equal in length to the radius of the circle. A full circle is 2π radians. Radians are often preferred in higher mathematics and physics because they simplify many formulas.
The conversion between them is straightforward: 180 degrees = π radians.
How to Use the Sine, Cosine, and Tangent Calculator
Our calculator simplifies the process of finding the sine, cosine, and tangent values for any given angle:
- Enter Angle Value: Input the numerical value of your angle into the "Angle Value" field.
- Select Angle Unit: Choose whether your angle is in "Degrees" or "Radians" from the dropdown menu.
- Calculate: Click the "Calculate" button.
The calculator will instantly display the sine, cosine, and tangent values for your specified angle.
Example Calculation
Let's calculate the trigonometric values for a 45-degree angle:
- Input: Angle Value = 45, Angle Unit = Degrees
- Calculation:
- Convert 45 degrees to radians: 45 * (π / 180) = π/4 radians.
- sin(π/4) = √2 / 2 ≈ 0.707107
- cos(π/4) = √2 / 2 ≈ 0.707107
- tan(π/4) = 1
- Output:
- Sine (sin): 0.707107
- Cosine (cos): 0.707107
- Tangent (tan): 1.000000
This calculator is a handy tool for students, engineers, and anyone needing quick and accurate trigonometric function values.