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This trigonometry calculator will help you in two popular cases when trigonometry is needed. If you want to find the values of sinecosinetangentand their reciprocal functionsuse 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 calculatorand 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 calculatorwhich 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:
- The first section takes an angle input and gives you a list of trigonometric function values for this angle. To input in a different unitclick on the unit to change itand then enter the angle.
For exampleto 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 functionssuch as cos(45°) and tan(45°).
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The second section uses trigonometry to determine the missing parameters of a right-angled triangle:
- Start entering the known parameters of the triangle into the calculatorand we will calculate the rest if such a triangle exists. For exampleinput the lengths of two sidesor an angle and one sideor an area and one side.
- Refer to the diagram at the top 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 unitchange the unit before entering a value.
- The tool will calculate the missing parameters using trigonometry.
For exampleif we know two sidesa = 7 cm and b = 12 cmwe enter them in this calculator. Right awaywe see that c = 13.892 cmα = 30.256°and β = 59.74°.
We can use this section in reversetoo! Say we know the angle β = 30°b = 10 inand c = 20 in. Firstenter β = 30°and instantly we learn that α = 60°. Nowenter b = 10 in (ensuring the unit is inches first). Similarlyinput c = 20 inand we see that a = 17.32 in.
If you're wondering how trigonometry can help you learn so much about trianglescontinue 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 suggeststrigonometry deals primarily with angles and triangles; in particularit defines and uses the relationships and ratios between angles and sides in triangles. The primary application is thus solving trianglesprecisely right trianglesand any other type of triangle you like.
🔎 Trigonometric functions (sincostan) are all ratios. Thereforeyou 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 systemastronomyand geography. Alsosine and cosine functions are fundamental for describing periodic phenomena — thanks to themwe can describe oscillatory movements (as in our simple pendulum calculator) and waves like soundvibrationor light.
🙋 Interested in knowing more about real-life applications of trigonometry? Check out our detailed article: When Will I Use Trigonometry in Real Life? Practical Applications Explained.
Many fields of science and engineering use trigonometry and trigonometric functionsnamely: musicacousticselectronicsmedicine and medical imagingbiologychemistrymeteorologyelectricalmechanicalcivil engineeringand 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 triangleall 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 anglesit'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 lengththen the triangles are congruent.
Meet the creator of our trigonometry calculator
HiI'm Hannathe brainchild of this trigonometry calculatorand 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 photographyso I sat down to create it. Thanks to thisI have captured some crisp photos of colorful birds in the wild!
We put extra care into the quality of our content so that it is 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 standardsplease check our Editorial Policies page.
FAQs
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What is trigonometry?
Trigonometry is the study of the relationships within a triangle. For right-angled trianglesthe ratio between any two sides is always the same and is given as the trigonometry ratioscossinand tan. Trigonometry can also help find some missing triangular informatione.g.the sine rule.
How to do trigonometry?
- Find which two of these you have: the hypotenuseadjacent or opposite sideor angle.
- Work out which of the remaining options you are trying to calculate.
- Choose which relationship you need (rememberSOHCAHTOA).
- Fill in the data you have into the equation.
- Rearrange and solve for the unknown.
- Check your answers with our trig calculator.
Is trigonometry hard?
Trigonometry can be hard at firstbut after some practiceyou will master it! Here are some trigonometry tips:
- Label the hypotenuseadjacentand 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 trianglesand right-angled triangles in particular. Since triangles are everywhere in naturetrigonometry is used outside of math in fields such as constructionphysicschemical engineeringand astronomy.
Who invented trigonometry?
Since trigonometry is the relationship between angles and sides of a triangleno one invented itit would still be there even if no one knew about it! The first people to discover part of trigonometry were the Ancient Egyptians and Babyloniansbut Euclid and Archemides first proved the identitiesalthough they did it using shapesnot algebra.
What grade is trigonometry taught at?
Trigonometry is usually taught to teenagers aged 13-15which 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 countryschooland pupils' ability.
How to convert decimal to degrees in trigonometry?
- Find which trigonometric relationship you are using with SOHCAHTOA.
- Take the inverse identity of your decimale.g.sin⁻¹(0.5).
- The resulting number is the degree of your angle.
- Check your results with our trigonometry calculators.
How to find the height of a triangle using trigonometry?
- Draw your triangle and mark the height. You will have to split the triangle into two smaller triangles.
- 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.
- Check your answers with Omni Calculator.
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