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Spell it, tap it, or draw it. Every output screen below shows the same text — edit or copy from whichever one you're next to.
1 · Type the name (type the symbol for the name)
Write theta to get θ, sup2 to get ², pi (π), or LaTeX code like \sin.
Plain words and LaTeX-style names both work — anything else is inserted as text.
LaTeX Screen
Code formatted for LaTeX documents ($ equations $).Quick Reference
- Theta:θ
- Squared:²
- Unicode (θ):
U+03B8 - LaTeX (θ):
\theta - LaTeX (²):
^2
Trigonometry Symbols & Identities Guide
Trigonometric identities are mathematical equations that relate the trigonometric functions (such as sine, cosine, tangent, cosecant, secant, and cotangent) to one another. These identities are true for all values of the variables (typically angles represented by the Greek letter theta, θ) where both sides of the equation are defined. They are crucial tools in calculus, physics, geometry, and advanced algebra for simplifying complex equations and integrations.
What is the Pythagorean Identity?
The primary Pythagorean trigonometric identity is:
This identity is derived directly from the **Pythagorean Theorem** in a right-angled triangle. In a unit circle (a circle with radius 1 centered at the origin), the coordinates of any point on the boundary are given by $(x, y) = (\cos\theta, \sin\theta)$, where $\theta$ is the angle. Because the hypotenuse is 1, the relation $x^2 + y^2 = 1^2$ translates directly to $\sin^2\theta + \cos^2\theta = 1$. This relation holds true for any real number value of the angle $\theta$.
Complete List of Trigonometric Identities
Below is a curated reference list of the most essential trigonometric identities used in science, technology, and engineering calculations:
| Identity Type | Mathematical Formulas | LaTeX Code |
|---|---|---|
| Pythagorean | sin²θ + cos²θ = 1 | \sin^2\theta + \cos^2\theta = 1 |
| Pythagorean (Tan/Sec) | 1 + tan²θ = sec²θ | 1 + \tan^2\theta = \sec^2\theta |
| Pythagorean (Cot/Csc) | 1 + cot²θ = csc²θ | 1 + \cot^2\theta = \csc^2\theta |
| Reciprocal | csc θ = 1 / sin θ | \csc\theta = \frac{1}{\sin\theta} |
| Reciprocal | sec θ = 1 / cos θ | \sec\theta = \frac{1}{\cos\theta} |
| Reciprocal | cot θ = 1 / tan θ | \cot\theta = \frac{1}{\tan\theta} |
| Quotient | tan θ = sin θ / cos θ | \tan\theta = \frac{\sin\theta}{\cos\theta} |
| Quotient | cot θ = cos θ / sin θ | \cot\theta = \frac{\cos\theta}{\sin\theta} |
| Angle Sum | sin(α+β) = sin α cos β + cos α sin β | \sin(\alpha+\beta) = \sin\alpha\cos\beta + \cos\alpha\sin\beta |
| Double Angle | sin(2θ) = 2 sin θ cos θ | \sin(2\theta) = 2\sin\theta\cos\theta |
How to Type These Symbols on Symbols Keyboard
Struggling to input scientific notation or specific mathematical symbols on a standard keyboard? Our online tool resolves this issue by providing instant autocompletion and conversion rules:
- Type
thetain the search bar above to get the Greek letter θ. - Type
sup2,squared, or2to recommend the superscript squared ². - Type
sinorcosto immediately output sine and cosine symbols. - Type
fracoroverto get layout suggestions and fraction templates.
Explore Other Scientific Keyboards
If you need to access other specialized datasets and keyboard layouts, feel free to use our collections:Math symbol keyboard,Physics constants keyboard,Chemistry formulas keyboard,Greek letters keyboard,Pi Symbol Page, andAll Symbols List.
Frequently Asked Questions (FAQ)
What is sin²θ + cos²θ equal to?
It is always equal to 1. This is the primary Pythagorean trigonometric identity, which holds true for any real angle value of θ.
How do I find the θ (theta) symbol?
You can find it on our main page or this page by typing "theta" in the search box. It will immediately show up as a suggestion, which you can click to copy.
What are the three Pythagorean identities?
The three basic Pythagorean trigonometric identities are:
1. sin²θ + cos²θ = 1
2. 1 + tan²θ = sec²θ
3. 1 + cot²θ = csc²θ