Trigonometric Equation Calculator

Solve trigonometric equations step-by-step.

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How to solve trigonometric equations step-by-step?

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Trigonometric Equations Calculator

Get detailed solutions to your math problems with our trigonometric equations step-by-step calculator . practice your math skills and learn step by step with our math solver. check out all of our online calculators here , solved problems, difficult problems.

Solved example of trigonometric equations

The reciprocal sine function is cosecant: $\frac{1}{\csc(x)}=\sin(x)$

Grouping terms

Combining like terms $8\sin\left(x\right)$ and $-4\sin\left(x\right)$

Divide both sides of the equation by $4$

The angles where the function $\sin\left(x\right)$ is $\frac{1}{2}$ are

The angles expressed in radians in the same order are equal to

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Trigonometric equations online calculator

The general form of trigonometric equation is

f ( trig ( x ) ) = 0

where - some arbitrary function, trig ( x ) - some trigonometric function.

As a rule, to solve trigonometric equation one need to transform it to the simplier form which has a known solution. The transformation can be done by using different trigonometric formulas .

For example, consider the solution of trigonometric equation

By using the cosine double angle formula, transform this equation to the simplier one:

The received equation is the very simple and has known solution. Our online calculator, build on Wolfram Alpha system is able to solve more complex trigonometric equations with step by step solution.

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Tool / solver to resolve one or more trigonometric equations, equations with unknown variables and cos, sin, tan, etc.

Trigonometric Equation Solver - dCode

Tag(s) : Symbolic Computation


dCode is free and its tools are a valuable help in games, maths, geocaching, puzzles and problems to solve every day! A suggestion ? a feedback ? a bug ? an idea ? Write to dCode !

Please, check our dCode Discord community for help requests! NB: for encrypted messages, test our automatic cipher identifier !

Feedback and suggestions are welcome so that dCode offers the best 'Trigonometric Equation Solver' tool for free! Thank you!

Answers to Questions (FAQ)

A trigonometric equation is a mathematical expression with an equality between two elements containing unknown variables and trigonometric functions (cos, sin, tan, etc.).

Example: $ \cos(x) = sin(\pi) $

dCode automatically solves the trigonometric equations (with the = equality symbol) and calculates the values of the unknowns.

All trig functions are supported: sin() , cos() , tan() , but also the trigonometry reciprocal functions acos() , arcsin() , and so on. as well as the hyperbolic functions cosh() , sinh() , etc.

Example: $ \sin(x) = 0 $ returns the solution $ x = 0 $ (radian)

Some equations will have an infinite number of solutions (modulo $ \pi $ or $ 2\pi $ or with constants $ c_i $)

All angles are in radian.

Multiple trig equations with the same variables can be combined with a logical AND operator: && or ⋀ .

Also, any new line return will be considered as a new equation.

The dCode solver does not display the calculation steps because they do not reflect the steps of a human thinking but to the steps of a machine thinking (bit-by-bit binary calculation operations) far from a hand-held resolution. dCode allows you to check a result.

Source code

dCode retains ownership of the "Trigonometric Equation Solver" source code. Except explicit open source licence (indicated Creative Commons / free), the "Trigonometric Equation Solver" algorithm, the applet or snippet (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or the "Trigonometric Equation Solver" functions (calculate, convert, solve, decrypt / encrypt, decipher / cipher, decode / encode, translate) written in any informatic language (Python, Java, PHP, C#, Javascript, Matlab, etc.) and all data download, script, or API access for "Trigonometric Equation Solver" are not public, same for offline use on PC, mobile, tablet, iPhone or Android app! Reminder : dCode is free to use.

The copy-paste of the page "Trigonometric Equation Solver" or any of its results, is allowed as long as you cite dCode! Exporting results as a .csv or .txt file is free by clicking on the export icon Cite as source (bibliography): Trigonometric Equation Solver on [online website], retrieved on 2023-03-15,

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Trigonometry Calculator: A New Era for the Science of Triangles

Mathematics is definitely among the top fears of students across the globe. Although the educational system presents numerous opportunities for students to enjoy developing new skills, excelling at sports, and practicing public speaking, it seems that nothing is working when it comes to mathematics.

Why is that, you may ask? Well, it depends.

First, our educational system is lacking in terms of intuitive and interactive learning.

How do you expect the students to enjoy studying a particular subject if they don’t even like the sessions?

Although there are some exceptions, most math teachers don’t (or maybe can’t) offer active lessons. Students, especially nowadays, prefer interaction, not passive learning. But who’s to blame here, really? Teachers are that way because their teachers were that way, and the same goes for those, in a continuous loop of flaws that govern the system.

On the other hand, students don’t appreciate math enough to give it their best. There’s always the question “When am I ever going to use this in real life?”, especially when it comes to specific math branches such as algebra and trigonometry.

Little do they know that a deeper understanding of mathematics as a subject can help them have a better understanding of your environment and the world around us. Math is the primary factor responsible for ameliorating your critical thinking and improving your problem-solving skills in your adulthood.

As a general rule of thumb, people who think mathematically are much faster thinkers than others who take a creative or artistic approach whenever they need to solve a problem.

While math lovers are more realistic and thoughtful, art lovers tend to live the moment and forget about the future and what it has to offer.

What is Trigonometry?

Trigonometry is the study of the properties of triangles, mainly the relationship between the angles and the length of the different sides.

Triangles are probably one of the most basic geometrical figures . Despite that, trigonometry has unveiled numerous applications with many practical, real-life uses, including, but not limited to, estimating bearings and accurate distances.

To validate calculations and perform operations, three fundamental functions are used in trigonometry: cosine, sine, and tangent. Essentially, the sin cos tan calculator on this page can help you here. Basically, if you know the measurements of two sides or angles, you can easily determine the measures of the rest.

When you say trigonometry, you say Pythagorean theorem; a formula that’s used to calculate the length of the different sides of a triangle.

In a triangle, the hypotenuse refers to the longest side, which faces the right angle. The remaining sides are known as the perpendicular and the base.

The Pythagorean theorem can be resumed in H²= B²+P², where H refers to the hypotenuse, B to the base, and P to the perpendicular (duh!).

Many formulas or identities can be derived from the theorem, which we will detail below.

If you have a hard time wrapping your head around those concepts, don’t worry, as our trig calculator can help you make these calculations a lot faster and easier.

Pythagorean Identities in Trigonometry

All trigonometric derivations and values are based on the Pythagorean Identities . While they may seem hard to memorize and understand, they’re actually quite the opposite, as you only need to practice them in a few questions to get the gist of them. Once you do that, applying these identities in different problems will become a piece of the pie.

There are 6 fundamental identities that you must learn for you to master trigonometry. These identities can prove useful in a handful of situations, be it inside or outside the school, and they are:

As with any other subject, it’s all about practice, so make sure to spend even as little as 30 minutes every day solving trigonometry problems if you want to master this subject. If you find an obstacle that you can’t bypass on your own, try our trigonometry calculator online to practice and familiarize yourself with the calculations.

Why Should You Learn Trigonometry?

Despite the widespread belief that math rules can only be used in school and during exams, mathematics , specifically trigonometry, has various real-life applications in nearly any industry such as business development, physics, design, etc.

Having a hard time believing that? Here’s a couple of the non-math related career paths in which you can find a great use for your trigonometrical skills.

Music and Trigonometry

As weird as that may seem, music is actually related to math. But, how?

To put it simply, sound travels in waves that resemble the graphical representation of the cosine and sine functions . In other words, what you hear every day while you’re going to school is nothing but a mere real-life representation of these trigonometric functions. I mean, how cool is that?

Using a trigonometry calculator sin cos tan allows engineers and producers to manipulate sound by altering sound wave patterns for different variables such as treble, volume, and base to get tunes that appeal to the listeners.

You’re probably familiar with T-pain and autotune. The well-known American rapper and singer reported that he has STUDIED autotune for a couple years before starting to use it in his music.

Video Games and Trigonometry

Take a look at games like Battlefield, Call of Duty, Far Cry, and God of War, and you’ll notice that they’re becoming more realistic with every release. The shadows, motion effects, graphics rendering, and all other elements of the game have never been better.

Why are we witnessing such amelioration? Because the developers are giving their best to improve physics engines, graphic, software, and programming by focusing on the properties of trigonometry. Mind blowing, huh?

In other words, if you’re into game development and want to get a career within that field, it’s time to start practicing math and trigonometry.

Space and Trigonometry

Have you ever watched a rocket launch? No? Then go check them out on YouTube, they’re astonishing.

Trigonometry is of the utmost importance when it comes to sending equipment, such as rockets and satellites, to outer space, as such operations require precise calculations of speed and bearings. The slightest miscalculation in this field can yield catastrophic results and failures, and even the loss of human lives, so there’s no room for mistakes.

So, if working alongside Elon Musk is a fantasy of yours, you better start practicing some trigonometry.

Digital Imaging and Trigonometry

We live in a digital world, where everything is governed by creative visuals, and when it comes to those, no one can deny the importance of trigonometry.

Digital imaging is what’s behind computers and visuals, and it’s all about measurements, calculations , and geometric patterns that determine how every pixel is displayed on your screen.

In other words, if you want to dive into the world of digital imaging and creativity in the years to come, you can’t ignore math and trigonometry.

Modern Architecture and Trigonometry

Every structure, curve, and calculation in modern architecture is precisely determined using different mathematical formulas, including trigonometric ones. Do you think those skyscrapers in Dubai got to the clouds on their own? No, you silly. They’re the result of countless hours of calculations and measurements.

Interior Design and Trigonometry

Just like architecture, interior design is also ruled by mathematical and trigonometric formulas that determine what fits where and whatnot to deliver a harmonic design all over the place.

So, there they are, some career paths that are governed by trigonometry despite not being directly related to mathematics. If you want a job in any of the mentioned fields, you have no choice but to give your best and study for your math classes.

How to Learn Trigonometry?

As hard as it may seem, learning trigonometry can actually be fun. All you need is a bit of determination and dedication, and you’re already ahead of 99% of students.

If you want to learn trigonometry the right way, you can follow this simple blueprint to success:

1.   Start With Simple Concepts

From the tiny acorn, grows the mighty oak, and from simple concepts, grow the bigger theorems. Start your journey towards trigonometry mastery by studying and practicing simple concepts to familiarize yourself with the basics. These include the six major identities mentioned above and their simple applications, along with the Pythagorean theorem and its uses.

2. Practice Deriving

Once you get the gist of the basics, you need to start practicing derivation . That way, you won’t have to memorize every single identity or formula, as you’ll be able to derive them on your own. Do that repeatedly, and derivation and identities will become second nature in no time.

Practice Different Types of Problems

Once you master derivation, you need to go further by moving to more complicated problems. That way, not only will you be able to memorize formulas, but you’ll understand how to pass from one concept to the other and how to employ each one of them without breaking a sweat.

3.Keep Practicing

Do you know how to perform addition and subtraction? Of course, you do. You’ve been doing it your whole life. So, if you want trigonometry to become second nature as well, you need to practice it continuously a following a preside studying plan. We highly recommend distributing your practice over the whole week rather than cramming several hours of studying into one day. That way, you’ll avoid boredom and get a higher studying frequency at the same time.

4. Organize Study Groups

When you’re in a group, you always try to give your best to avoid showing up as the weakest, which makes study groups an excellent way to give your best while practicing trigonometry. Besides, you’ll get great value out of the verbal interchange during the session.

5.if You Need Help, Don’t Hesitate to Ask

If you get stuck while you’re trying to solve a specific problem, do not hesitate to ask your teacher or instructor for help. If they’re not available, you can visit our trigon calculator as it can show you the step-by-step process that leads to every result.

Why Use the online trigonometry calculator?

There are many reasons as to why you should use our trigonometry graphing calculator. For starters, it’s extremely easy to use, and you don’t have to spend hours trying to figure out what every button does, which is the case when using a standard scientific or graphing calculator.

We highly recommend using Mathway’s trigonometry triangle calculator if:

We get it. You don’t want to use a graphing calculator because they’re a bit of a burden to keep carrying around. After all, why would you do so if you can simply use an app on your phone?

The problem with apps though is that they take up space on your smartphone or tablet and they can make your device a bit laggy. If you’d rather stay away from such issues, you can simply use our online tool, which is considered as the best calculator for trigonometry. Why? Because it’s compatible with any electronic device, making it superior to apps that you have to download and install. With our triangle trigonometry calculator, solving your math problems is just a few clicks away.

Also – It’s basically an online trig calculator app.

Are you stuck and couldn’t find a way to solve that homework your teacher gave you? Can’t find a tutor to show you the way? No problem, just sign up with Mathway and let the right triangle trigonometry calculator show you how to solve any problem step by step.

Not only can SolveMathPorblems’ solve any problem you through at it, but it can also show you the steps that led to the result. That way, you can identify your mistakes and fix them so that you can improve and push your trigonometry skills to the next level.

Remember, don’t check the result until you try solving the problem and answering your questions yourself. Otherwise, you’re only cheating yourself. Math isn’t about fooling the teacher into believing that you did a great job, it’s about unveiling your mistakes and working on your flaws. That’s why we’ve got this trig calc.

Who said math is hard? Mathematics isn’t actually about complicating things; it’s about simplifying complicated problems and breaking them down into small chunks that you can solve one step at a time. Knowing that what applies to math, in general, goes for trigonometry as well, you’ll be content to hear that our trigonometry online calculator can simplify complex problems and solve them through the easiest of ways, thus teaching you the logical process behind every solution.

One can find himself without a scientific calculator for a variety of reasons

Why Is the Trigonometry Calculator Online?

Being an online app, not only can our Trigonometry calculator work on any device without any downloading or installation, but it can also be used anywhere, anytime. That way, you can practice problem-solving whenever you feel like it without carrying a bulky scientific calculator with you everywhere you go.

Why Is the Trigonometry Calculator Free?

There are only a few things in this world that any one of us can consider to be priceless. Knowledge is most definitely one of them. Today, students across the globe, especially in scientific fields, are in need of aid in getting a good grasp of the essential and basic skills and tools that are required for their studies.

So when it comes to anything related to math and trigonometry, we’d like to offer as much assistance as we can. In the matter that we have at hand, we think that by providing this trig calculator (with its usage guide) to all the students around the world, we’ll be able to do the least we can in our quest for bringing knowledge to everyone in the most suitable way. And, by the way, we’re giving away this trig calculator online for free.

Hopefully, your search for a free trigonometry calculator will come to an end with what we have to offer. Keep your money in your pocket and enjoy learning with our free service.

What Can a Trigonometry Calculator Do?

Basically, a whole lot of things. Some might come in with the assumption that because it is an internet service that it cannot deliver on the same level of versatility that a regular calculator does. But that would be wrong. This online trig calculator with steps can provide multiple utilities that would satisfy all your mathematical necessities, regardless of your level. Our app can work as a:

It’s not just a good trig calculator; it’s the best trigonometry calculator.

Trigonometry Calculator: Symbols

If you go on and take a look at what the interface of our calculator has to offer, you’ll come to find that it encompasses a large number of symbols. Now you can see some of them in any standard calculator, but some others are specific only to our calculator.

You’ll find symbols such as the division sign, rectangular pyramid, cylinder, trapezoid, triangle, equal to or less than, square roots, exponents, fractions, absolute value , and parenthesis among other things. Because of that, we’re confident enough to say that this calculator isn’t only the best trigonometry value calculator, but also the best inverse trigonometry calculator.

The versatility that this calculator brings makes it perfect for everything from college work, homework, testing and answer verification. So let’s say you’ve got some time to spare, you can take your Smartphone out of your pocket, go to the website and hone your trigonometry skills through problem-solving. Even if you don’t have any problems at your disposal, you can choose from our pre-existing list of examples.

Using a Calculator for Trigonometry

If you go around searching for a guideline for using a calculator for trigonometry, you probably won’t have any luck in finding anything useful. We’ll try sparing you the useless search for such a thing on the internet and give you a simple explanation of how to use the calculator so you can jump right to doing your homework. Here’s how it’s done:

If you happen to have made a mistake, make a note of it and practice on avoiding it in the future. If you feel like you need to see the detailed steps, all you have to do is sign up for Mathway.

So, Who Made This Trigonometry Calculator?

The brilliant work that’s been done to bring this magnificent app to life comes all from the minds of the people at Mathway. It’s only here on our website to make it easy for everyone around the world to have access to it. If you’re interested in getting the full potential of this app , you’ll have to sign up. But don’t let that deter you; it’s actually pretty simple and quick. Just make sure to have your parents’ approval if you’re underage.

This is the app you need in your arsenal if you’re looking to push yourself and improve your skills in problem-solving. It’s a free and useful calculator that has all the stuff that you’ll need to solve any trigonometry problem. From sine and cosine to the fundamental Pythagorean theorem, this is the tool that you’ll want to have by your side, or, more accurately, in your pocket.

Trigonometry, which studies the measure of triangles, takes algebra to the next level. Its most well-known features include the Pythagorean Theorem and the sine, cosine, and tangent ratios. Our trig calculator can help you check problems that involve these relationships as well as many others. Simply enter your problem into this advanced calculator to see if you worked it correctly.

Not only can this advanced calculator check answers but it can also provide additional practice problems to help hone your skills in preparation for tests and quizzes. To use this feature, find the type of problem you want to practice in the Examples section. Click on the desired topic, and an example problem will appear in the calculator screen. Click the Show button to see the problem in its standard format or as a picture if applicable. Solve the problem and click Answer to see if you are right.

Quick Trig Facts

Pythagorean theorem.

\large c^2 = a^2 + b^2

Trig Ratios

\large \sin \theta \frac{opp}{hyp}

Law of Sines

\large \frac {a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}

Law of Cosines

\large c^2 = a^2 + b^2 - 2ab \cos C

Reference Triangles

trig references triangles

Trigonometry Tips

How to Use the Calculator

Starting with an Example

Trigonometry Calculator Symbol Guide


Note: If no index is given, it is assumed to be two and is just called a square root.


Note : If no subscript (base) is given, the base is assumed to be 10.



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