Trig Calculator: Solve Trigonometry Problems

A Trig Calculator (Trigonometry Calculator) is a free online Maths calculator. It can calculate all the Trigonometric functions of Sin, Cos and Tan to make it easier for you to calculate Trigonometry problems.

Trigonometry is a branch of maths which looks at the relations between angles and sides in triangles. It can be used in many areas including Geometry, Algebra, Physics, Engineering, Architecture, Building and Navigation.

There are three main Trigonometric functions:

Sine (sin): Opposite / Hypotenuse.

Cosine (cos): Adjacent / Hypotenuse.

Tangent (tan): Opposite / Adjacent.

The free Trig Calculator will help you calculate the values of these functions without having to do any complex Maths problems. All you need to do is put in the angle you wish to calculate.

This can be useful for students in the US as they can use it to help with their high school Geometry, Algebra, Pre-calculus and Calculus problems. It can also help students prepare for Standardised Maths Exams such as the

SAT and ACT.

It can be used to calculate various problems including Homework, triangle measurements and Engineering.

How to Use the Trig Calculator

Using the online Trig Calculator is simple and does not require any complex Maths knowledge.

Simply type in the angle you wish to calculate.

Type in the angle (e.g. 30, 45 or 60).

Choose if the angle is in Degrees or Radians.

Choose the Trigonometric function (Sine, Cosine or Tangent).

Click the Calculate button.

The calculator will show you your result.

Reset the calculator or change the angle and function to calculate another problem.

Example:

If you want to find the sine of 30 degrees:
Angle: 30
Unit: Degrees
Function: Sine
This will give you:
sin(30°) = 0.5

You can use this method to calculate cosine and tangent.

Trig Calculator Formula

There are various formulas you can use in Trigonometry.

The 3 main Trigonometric Ratios can be calculated using a right angled triangle.

\\(\\sin(\\theta)=\\frac{\\text{opposite}}{\\text{hypotenuse}}\\)
Drag the pointsθ36.9°53.1°Adjacent 4Opposite 3Hypotenuse 5
Feedback
Sine
sin(θ) = Opposite / Hypotenuse
Cosine
cos(θ) = Adjacent / Hypotenuse
Tangent
tan(θ) = Opposite / Adjacent

Another important Trigonometric formula is:

sin 2(θ) + cos 2(θ) = 1

This can be useful to check your Trigonometric calculations.

Converting Degrees to Radians

Radians = Degrees x π/180
Converting Radians to Degrees
Degrees = Radians x 180/π

Understanding the formulas will help you calculate Trigonometric values.

Example Calculation

Let’s look at an example to understand how the Trig Calculator works.
Calculate the sine, cosine and tangent of 45 degrees.

Firstly type in the angle:

θ = 45°
Secondly calculate the sine:
sin(45°) = √2 / 2
sin(45°) ≈ 0.7071
Thirdly calculate the cosine:
cos(45°) = √2 / 2
cos(45°) ≈ 0.7071
Finally calculate the tangent:
tan(45°) = sin45° / cos45°
tan(45°) = 1
Final Answer
Function Result
Sin 45° 0.7071
Cos 45° 0.7071
Tan 45° 1.0000

This shows how the Trigonometric functions can calculate the relationships between the angles and sides of a right angled triangle.

Understanding your Answer

The answer shown on the Trig Calculator will show you the value of the Trigonometric function you have chosen for the angle you have inputted.
Depending on the function you have chosen, the answer will mean something different.

For Sine: This will show the ratio of the opposite side to the hypotenuse.

For Cosine: This will show the ratio of the adjacent side to the hypotenuse.

For Tangent: This will show the ratio of the opposite side to the adjacent side.

For Sine and Cosine answers will always be between -1 and 1 for real angles.

Answers for Tangent can be any real number. However, the tangent will be undefined for certain angles like 90° and 270° as the cosine will be 0.

You may also get answers given as decimals, fractions or exact values.

For example:
sin(30°) = 0.5

This means that the opposite side is half the length of the hypotenuse in a right angled triangle with an angle of 30°.

Factors Affecting the Answer

There are a few factors you should consider when using the Trig Calculator.

Angle

The angle you put in will affect the Trigonometric answer. If you change the angle by even a little bit, you will get a different answer for sine, cosine or tangent.

Degrees or Radians

Angles can be measured in degrees or radians. If you choose the wrong one you will get the wrong answer.

For example:

sin(30°) = 0.5

However, 30 radians is a completely different angle.

Trigonometric Function

Depending on the function you choose, you will get a different answer. Sine, cosine and tangent all calculate different relationships.

Angles

As Trigonometric functions are periodic, you can get answers for angles over 360 degrees or negative angles.

Calculator Accuracy

Some calculators will round the answer to 4 decimal places or more. This may make the answer slightly different to the exact value.

Undefined Values

Some angles will cause the tangent to be undefined.

Incorrect Values

If you put in incorrect angles, miss out decimal places or choose the wrong unit you will get an incorrect answer.

Benefits of Using a Trig Calculator

There are many benefits to using an online Trig Calculator.

• Time Saving: You can calculate the Trigonometric values in a matter of seconds.
• Student Friendly: Students can use it to help with their homework whilst studying Geometry, Algebra, Pre-calculus and Calculus.
• Useful for SAT and ACT: You can use Trigonometry concepts to help with your Maths in Standardised exams in the US.
• Engineering: Engineers use Trigonometric functions to calculate angles, distances, forces and measurements of components.
• Architecture: Architects use Trigonometry to plan buildings, roof angles, slopes and designs.
• Construction: Construction professionals can calculate roof pitches, stair angles, elevations and measurements.
• Physics: Trigonometry can help you calculate vectors, projectile motion, wave patterns and forces.
• Navigation: Trigonometry calculations can help you calculate distances, directions, elevations and positions.
• Easy to Access: Most Trig Calculators on the internet will work on your desktop, laptop, tablet and smartphone.

Accuracy, Assumptions and Limitations

If you put in the correct angle, unit and function then the calculator can give you accurate results.

However there are some assumptions and limitations you should be aware of:

Correct Values: If you put in incorrect angles or choose the wrong function you may get unexpected results.

Units: Always double check you have chosen the right unit (degrees or radians).

Rounded Decimals: Answers may be rounded if they are given as decimals. You may get more accurate answers if you use exact fractions or symbols.

Undefined: Tangent will be undefined if the cosine of the angle is 0.

Right Angled Triangles: The basic Trigonometric ratios (SOH-CAH-TOA) only apply to right angled triangles. However Trigonometric functions can be extended to other angles using the unit circle.

Floating Point: There may be slight differences in the answer due to floating point calculations.

Some basic calculators may not have the option to calculate inverse

Trigonometric functions, Hyperbolic functions or complex numbers.
If you are doing any important work for your studies, engineering or science always double check you have put in the correct values and that the calculator can perform what you need.

FAQs

What is a Trig Calculator?

A Trig Calculator is an online Maths calculator which can calculate Trigonometric functions such as Sine, Cosine and Tangent. It can help you solve problems involving angles and understand the relationships between the sides of triangles.

Is it free to use?

Many online Trig Calculators are completely free to use. You can calculate Sine, Cosine and Tangent values without having to pay for extra software.

What is the difference between degrees and radians?

Angles can be measured in degrees or radians. There are 360 degrees in a full circle or \\(2\\pi\\) radians. They both measure the same angles but just in different units.

Can I calculate Sine, Cosine and Tangent?

Yes! A standard Trig Calculator can calculate Sine, Cosine and Tangent. Some advanced calculators can also calculate inverse Trigonometric functions such as Arcsine, Arccosine and Arctangent.

Can I use it on my smartphone?

Most online Trig Calculators can be used on your smartphone, tablet, laptop and desktop. Just open up a modern web browser!