Trigonometry Calculator
Free Trigonometry Calculator for math. Enter values to solve step-by-step with verified formulas, worked examples, and detailed explanations.
Formula
sin(ฮธ) = Opp/Hyp
Trigonometric functions relate angles to side ratios in right triangles.
Worked Examples
Example 1: Sin(30ยฐ)
Problem:Angle 30 degrees
Solution:Opposite side is half the hypotenuse.
Result:0.5
Example 2: Tan(45ยฐ)
Problem:Angle 45 degrees
Solution:Opposite equals Adjacent.
Result:1
Frequently Asked Questions
What is Trigonometry?
It is the branch of mathematics dealing with the relationships between the sides and angles of triangles.
How is trigonometry used in real life?
It is used in architecture, engineering, astronomy, music production (sound waves), game development (graphics), and navigation.
Background & Theory
**Trigonometric Functions:**
Relate the angles of a right triangle to the ratios of its side lengths.
**Primary Ratios (SOH CAH TOA):**
* **Sine (sin ฮธ):** Opposite / Hypotenuse
* **Cosine (cos ฮธ):** Adjacent / Hypotenuse
* **Tangent (tan ฮธ):** Opposite / Adjacent
**Unit Circle:**
A circle with radius 1 centered at the origin.
* x-coordinate = cos(ฮธ)
* y-coordinate = sin(ฮธ)
**Modes:**
* **Degrees:** Circle = 360ยฐ
* **Radians:** Circle = 2ฯ radians (approx 6.28)
History
Trigonometry ("triangle measurement") emerged in the Hellenistic world during the 3rd century BC from applications of geometry to astronomical studies. Hipparchus (c. 190-120 BC) compiled the first trigonometric table. The modern sine function was first defined in the Surya Siddhanta in ancient India, and later advanced by Islamic mathematicians like Al-Khwarizmi.