Sin Tan Cos Calculator – Loan calculator

Sine, Cosine, Tangent Calculator

Angle Value:

Angle Unit: Degrees Radians

Sine:

Cosine:

Tangent:

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Understanding Sine, Cosine, and Tangent

Sine (sin), Cosine (cos), and Tangent (tan) are fundamental trigonometric functions that describe the relationships between the angles and sides of a right-angled triangle. They are crucial in various fields, including mathematics, physics, engineering, and computer graphics.

What Do They Represent?

For a right-angled triangle with an angle θ (theta):

Sine (sin θ): The ratio of the length of the side opposite the angle to the length of the hypotenuse. (SOH – Sine = Opposite / Hypotenuse)
Cosine (cos θ): The ratio of the length of the side adjacent to the angle to the length of the hypotenuse. (CAH – Cosine = Adjacent / Hypotenuse)
Tangent (tan θ): The ratio of the length of the side opposite the angle to the length of the side adjacent to the angle. (TOA – Tangent = Opposite / Adjacent)

These definitions are extended to all angles (not just acute angles in a right triangle) using the unit circle, where the hypotenuse is always 1, and the adjacent and opposite sides correspond to the x and y coordinates of a point on the 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 defined by the angle subtended at the center of a circle by an arc equal in length to the radius. 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.

Why Are These Functions Important?

Trigonometric functions are indispensable for:

Physics: Describing wave motion, oscillations, projectile trajectories, and forces.
Engineering: Structural analysis, signal processing, electrical engineering, and robotics.
Computer Graphics: Calculating rotations, transformations, and rendering 3D objects.
Navigation and Astronomy: Determining positions, distances, and celestial movements.
Mathematics: Solving complex equations, analyzing periodic phenomena, and in calculus.

How to Use the Calculator

Our Sine, Cosine, Tangent Calculator simplifies the process of finding these 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.
Click "Calculate": The calculator will instantly display the sine, cosine, and tangent values for your specified angle.

Examples:

Angle: 0 Degrees
- Sine: 0
- Cosine: 1
- Tangent: 0
Angle: 90 Degrees
- Sine: 1
- Cosine: 0
- Tangent: Undefined (because division by zero, as cos(90°) = 0)
Angle: 45 Degrees
- Sine: 0.70710678
- Cosine: 0.70710678
- Tangent: 1
Angle: π Radians (180 Degrees)
- Sine: 0
- Cosine: -1
- Tangent: 0

This calculator is a handy tool for students, engineers, and anyone needing quick and accurate trigonometric calculations.