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Trigonometry Calculator

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How to use this trigonometry calculatorWhat is trigonometry?Trigonometry calculator as a tool for solving right triangleMeet the creator of our trigonometry calculatorFAQs

This trigonometry calculator will help you in two popular cases when trigonometry is needed. If you want to find the values of sine, cosine, tangent, and their reciprocal functions, use the first part of the calculator. Are you searching for the missing side or angle in a right triangle using trigonometry? Our tool is also a safe bet! Type 2-3 given values in the second part of the calculator, and you'll find the answer in a blink of an eye. Scroll down if you want to learn about trigonometry and where you can apply it.

There are many other useful tools when dealing with trigonometry problems. Check out two popular trigonometric laws with the law of sines calculator and our law of cosines calculator, which will help you to solve any kind of triangle.

How to use this trigonometry calculator

This trigonometry calculator has two sections that perform two different functions using trigonometry. The following instructions should help you work your way around this calculator with ease:

  1. The first section takes an angle input and gives you a list of trigonometric function values for this angle. To input in a different unit, click on the unit to change it, and then enter the angle.

For example, to find the value of sin(45°), we merely enter 45 degrees as the angle. The calculator instantly tells you that sin(45°) = 0.70710678. It also gives the values of other trig functions, such as cos(45°) and tan(45°).

  1. The second section uses trigonometry to determine the missing parameters of a right-angled triangle:

    1. First, select what parameters are known about the triangle. You can choose between "two sides", "an angle and one side", and "area and one side".

    2. Refer to the diagram at the bottom of the calculator to understand the parameter labels. Enter the parameters based on your choice. If you need to input a parameter in a different unit, change the unit before entering a value.

    3. The tool will calculate the missing parameters using trigonometry.

For example, if we know two sides, a = 7 cm and b = 12 cm, we enter them in this calculator. Right away, we see that c = 13.892 cm, α = 30.256°, and β = 59.74°.

We can use this section in reverse, too! Say we know the angle β = 30°, b = 10 in, and c = 20 in. First, enter β = 30°, and instantly we learn that α = 60°. Now, enter b = 10 in (ensuring the unit is inches first). Similarly, input c = 20 in, and we see that a = 17.32 in.

If you're wondering how trigonometry can help you learn so much about triangles, continue reading this article. It answers many questions that people new to trigonometry should know.

What is trigonometry?

Trigonometry is a branch of mathematics. The word itself comes from the Greek trigōnon (which means "triangle") and metron ("measure"). As the name suggests, trigonometry deals primarily with angles and triangles; in particular, it defines and uses the relationships and ratios between angles and sides in triangles. The primary application is thus solving triangles, precisely right triangles, and any other type of triangle you like.

🔎 Trigonometric functions (sin, cos, tan) are all ratios. Therefore, you can find the missing terms using nothing else but our ratio calculator!

Trigonometry has plenty of applications: from everyday life problems such as calculating the height or distance between objects to the satellite navigation system, astronomy, and geography. Also, sine and cosine functions are fundamental for describing periodic phenomena - thanks to them, we can describe oscillatory movements (as in our simple pendulum calculator) and waves like sound, vibration, or light.

trigonometric functions in a right triangle

Many fields of science and engineering use trigonometry and trigonometric functions, namely: music, acoustics, electronics, medicine and medical imaging, biology, chemistry, meteorology, electrical, mechanical, civil engineering, and even economics... The trigonometric functions are really all around us!

Trigonometry calculator as a tool for solving right triangle

To find the missing sides or angles of the right triangle, all you need to do is enter the known variables into the trigonometry calculator. You need only two given values in the case of:

  • one side and one angle
  • two sides
  • area and one side

Remember that if you know two angles, it's not enough to find the sides of the triangle. Two triangles having the same shape (which means they have equal angles) may be of different sizes (not the same side length) - that kind of relationship is called triangle similarity. If the sides have the same length, then the triangles are congruent.

Meet the creator of our trigonometry calculator

Hi, I'm Hanna, the brainchild of this trigonometry calculator, and I'm a doctor of mechanical engineering and a maestro at creating scientific tools. I knew a good trigonometry calculator would help me get the right depth of field for my photography, so I sat down to create it. Thanks to this, I have captured some crisp photos of colorful birds in the wild!

We put extra care into the quality of our content so that they are as accurate and reliable as possible. Each tool is peer-reviewed by a trained expert and then proofread by a native speaker. To learn more about our standards, please check the Editorial Policies page.


What is trigonometry?

Trigonometry is the study of the relationships within a triangle. For right-angled triangles, the ratio between any two sides is always the same and is given as the trigonometry ratios, cos, sin, and tan. Trigonometry can also help find some missing triangular information, e.g., the sine rule.

How to do trigonometry?

  1. Find which two of these you have: the hypotenuse, adjacent or opposite side, or angle.
  2. Work out which of the remaining options you are trying to calculate.
  3. Choose which relationship you need (remember, SOHCAHTOA).
  4. Fill in the data you have into the equation.
  5. Rearrange and solve for the unknown.
  6. Check your answers with our trig calculator.

Is trigonometry hard?

Trigonometry can be hard at first, but after some practice, you will master it! Here are some trigonometry tips:

  • Label the hypotenuse, adjacent, and opposite sides on your triangle to help you figure out what identity to use.
  • Remember the mnemonic SOHCAHTOA for the trigonometric relationships!

What is trigonometry used for?

Trigonometry is used to find information about all triangles, and right-angled triangles in particular. Since triangles are everywhere in nature, trigonometry is used outside of math in fields such as construction, physics, chemical engineering, and astronomy.

Who invented trigonometry?

Since trigonometry is the relationship between angles and sides of a triangle, no one invented it, it would still be there even if no one knew about it! The first people to discover part of trigonometry were the Ancient Egyptians and Babylonians, but Euclid and Archemides first proved the identities, although they did it using shapes, not algebra.

What grade is trigonometry taught at?

Trigonometry is usually taught to teenagers aged 13-15, which is grades 8 & 9 in the USA and years 9 & 10 in the UK. The exact age at which trigonometry is taught depends on the country, school, and pupils' ability.

How to convert decimal to degrees in trigonometry?

  1. Find which trigonometric relationship you are using with SOHCAHTOA.
  2. Take the inverse identity of your decimal, e.g., sin⁻¹(0.5).
  3. The resulting number is the degree of your angle.
  4. Check your results with our trigonometry calculators.

How to find the height of a triangle using trigonometry?

  1. Draw your triangle and mark the height. You will have to split the triangle into two smaller triangles.
  2. Solve either of these remaining triangles using regular trigonometry to find the height. The opposite or adjacent will now be the hypotenuse of the smaller triangle.
  3. Check your answers with Omni Calculator.

Trigonometric functions: sin, cos, tan...

...or trigonometry in right triangle

Diagram illustrating the trigonometry in a right triangle.
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