Sine and Cosine Calculators Hub
The sine and cosine functions are the backbone of trigonometry, geometry, statistics, and engineering. Whether you’re solving angles in a triangle, working with machine learning vector similarity, or studying signal processing, these calculators make it easy to compute accurate results with formulas, tables, and step-by-step guides.
Below you’ll find all sine calculators and all cosine calculators, grouped by type.
🔹 Sine Calculators
Sine Plate Calculator
Used in machining and angle measurement with sine plates.
Sine Bar Calculator
Helps machinists find angles using sine bars.
Sine Block Calculator
Angle setting using precision sine blocks.
Fourier Sine Series Calculator
Function expansion using sine terms for signal processing.
sin⁻¹ (Inverse Sine) Calculator
Find the angle when sine value is known.
🔹 Cosine Calculators
Cosine & Inverse Cosine Calculator
Find cos(θ) or θ from a cosine value.
Law of Cosines Calculator
Solve triangles using side/angle inputs.
Law of Cosines Triangle Calculator
Alternate tool for oblique triangle calculations.
Cosine Similarity Calculator
Compare vector similarity in ML and data science.
Cosine Distance Calculator
Find vector dissimilarity in clustering and statistics.
Fourier Cosine Series Calculator
Expand functions into cosine terms.
Hyperbolic Cosine Calculator
Compute cosh(x) for physics and advanced math.
🔹 How It Works
Sine function:
sinθ = opposite / hypotenuse
Cosine function:
cosθ = adjacent / hypotenuse
Inverse functions:
θ = sin⁻¹(x)
θ = cos⁻¹(x)
Law of Cosines:
c² = a² + b² - 2ab cos(C)
Cosine Similarity:
Similarity = (A · B) / (||A|| ||B||)
Cosine Distance:
Distance = 1 - Similarity
Fourier Sine/Cosine Series:
Expands functions into infinite sine or cosine series for signal processing.
Hyperbolic Cosine:
cosh(x) = (eˣ + e⁻ˣ) / 2
🔹 Quick Reference Table
| Calculator | Formula / Use Case |
|---|---|
| Sine & Inverse Sine | θ = sin⁻¹(x) |
| Cosine & Inverse Cosine | θ = cos⁻¹(x) |
| Law of Cosines | c² = a² + b² - 2ab cos(C) |
| Cosine Similarity | (A · B) / (||A|| ||B||) |
| Cosine Distance | 1 - Similarity |
| Fourier Sine Series | f(x) = Σ bₙsin(nπx/L) |
| Fourier Cosine Series | f(x) = a₀/2 + Σ aₙcos(nπx/L) |
| Hyperbolic Cosine | cosh(x) = (eˣ + e⁻ˣ) / 2 |
🔹 FAQs
- Q1. What’s the difference between sine and cosine?
- A: Sine relates to the opposite side of a right triangle, while cosine relates to the adjacent side.
- Q2. When do I use law of cosines vs law of sines?
- A: The law of cosines is used for oblique triangles (no right angles) when you have two sides and the included angle, or all three sides.
- Q3. What is cosine similarity used for?
- A: It’s used in machine learning, text mining, and clustering to measure the similarity between two non-zero vectors in an inner product space.
- Q4. Why do we use Fourier sine and cosine series?
- A: They allow periodic functions to be expressed as infinite sums of sines and cosines, which is essential for analyzing signals and solving differential equations in engineering and physics.
- Q5. What is hyperbolic cosine?
- A: It’s a hyperbolic function that models the shape of a hanging cable or chain (a catenary) and is used in various fields of physics and engineering.