Trigonometry Calculator
Enter an angle to get its main trigonometric functions: sine, cosine, and tangent.
Trigonometric calculations with a right triangle.
Table of Contents
Need to solve trigonometric functions or find the sides and angles of a right triangle? This trigonometry calculator is designed to help with both. It's perfect for students and professionals looking for a fast and accurate solution.
What can you do with this calculator?
✅ Calculate basic trigonometric functions
Enter an angle and you'll instantly get the values for sine, cosine, tangent, and also their reciprocal functions: cosecant, secant, and cotangent. You can work in degrees or radians, depending on your needs.
✅ Solve right triangles
Missing a side or an angle? You only need to know 2 or 3 values of the triangle (sides or angles), and the calculator will do the rest. You'll instantly get the missing elements using trigonometric ratios.
How to use it?
This tool has two sections:
Trigonometric functions:
- Enter an angle and select the unit (degrees or radians).
- The calculator will display the values of all common trigonometric functions for that angle.
Triangle solving:
- Choose the known values: two sides, one side and one angle, or area and one side.
- Enter the values based on the reference diagram.
- The calculator will automatically find the missing sides and angles.
For example, if you enter a = 6 and b = 8, you'll instantly get c ≈ 10, along with the internal angles. You can also work in reverse: if you know an angle and a pair of sides, you can easily find the rest.
What is trigonometry?
Trigonometry is a branch of mathematics that studies the relationships between the sides and angles of triangles, especially right-angled ones. Its main functions –sine, cosine, and tangent– help solve practical problems in geometry, physics, architecture, and more.
These functions are also essential in periodic phenomena such as waves, sound, light, and oscillatory motion. Thanks to trigonometry, we can design everything from bridges to GPS navigation systems.
Frequently Asked Questions
What does trigonometry study?
Trigonometry focuses on analyzing the relationships between the sides and angles of triangles. The main functions —sine, cosine, and tangent— allow you to solve all types of triangles, especially right-angled ones.
How can I solve a triangle using trigonometry?
First, identify the known values: a side and an angle, or two sides. Then choose the appropriate trigonometric ratio (e.g., sin, cos, or tan) and plug in the values. Finally, isolate the unknown and solve.
Why is trigonometry considered difficult?
At first, it may seem complicated due to the number of formulas and new terms. But with practice and visual examples, many people grasp it easily. Don't forget to use aids like the SOHCAHTOA mnemonic.
In what real-life situations is trigonometry used?
Trigonometry is used in architecture, engineering, astronomy, navigation, robotics, computer graphics, and more. Whenever there's a need to measure angles or distances indirectly, it's very useful.
Who were the first to use trigonometric principles?
Ancient Egyptians and Babylonians already applied trigonometric concepts to build pyramids and observe the skies. Later, Greek mathematicians like Hipparchus and Ptolemy formalized these principles.
At what age or school level is trigonometry taught?
In most countries, trigonometry is introduced during secondary education, usually between 13 and 15 years old, once students are familiar with basic geometry.
How do you convert a trigonometric ratio to an angle?
If you have a decimal value, such as 0.866, you can use the inverse function. For example: arccos(0.866) or cos-1(0.866) will give you the angle in degrees or radians.
What are the steps to calculate a triangle's height using trigonometry?
Draw the triangle and identify the known angle and side. Use a trigonometric function like sin(θ) = height / hypotenuse. Rearrange the formula and compute: height = hypotenuse × sin(θ).