Trig Calculator

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Trig Calculator
Sine (sin)Cosine (cos)Tangent (tan)Inverse Sine (arcsin)Inverse Cosine (arccos)Inverse Tangent (arctan)Cosecant (csc)Secant (sec)Cotangent (cot)
Degrees (°)Radians (rad)
<button type="reset" onclick="document.getElementById('answer').innerHTML='
'" style="background:#f5f5f5;color:#333;padding:12px 30px;border:1px solid #ccc;border-radius:3px;font-size:16px;cursor:pointer;">Clear
Result:

Enter values and click Calculate
function updateLabels(){var mode=document.getElementById('given_data').value;var l1=document.getElementById('label1');if(mode.startsWith('a')){l1.innerHTML='Value (x):';}else{l1.innerHTML='Angle (θ):';}}function calculateTrig(){var mode=document.getElementById('given_data').value;var v1=parseFloat(document.getElementById('input1').value);var unit=document.getElementById('unit_type').value;var showSteps=document.getElementById('steps').checked;if(isNaN(v1)){alert('Please enter a valid numeric value');return;}var res=0;var formula="";var inputDisplay=v1+(unit==='deg'?'°':' rad');if(mode==='sin'){var rad=(unit==='deg')?v1*(Math.PI/180):v1;res=Math.sin(rad);formula="sin("+inputDisplay+")";}else if(mode==='cos'){var rad=(unit==='deg')?v1*(Math.PI/180):v1;res=Math.cos(rad);formula="cos("+inputDisplay+")";}else if(mode==='tan'){var rad=(unit==='deg')?v1*(Math.PI/180):v1;res=Math.tan(rad);formula="tan("+inputDisplay+")";}else if(mode==='asin'){if(v11){alert('Input for arcsin must be between -1 and 1′);return;}res=Math.asin(v1);if(unit==='deg')res=res*(180/Math.PI);formula="arcsin("+v1+")";}else if(mode==='acos'){if(v11){alert('Input for arccos must be between -1 and 1′);return;}res=Math.acos(v1);if(unit==='deg')res=res*(180/Math.PI);formula="arccos("+v1+")";}else if(mode==='atan'){res=Math.atan(v1);if(unit==='deg')res=res*(180/Math.PI);formula="arctan("+v1+")";}else if(mode==='csc'){var rad=(unit==='deg')?v1*(Math.PI/180):v1;res=1/Math.sin(rad);formula="1 / sin("+inputDisplay+")";}else if(mode==='sec'){var rad=(unit==='deg')?v1*(Math.PI/180):v1;res=1/Math.cos(rad);formula="1 / cos("+inputDisplay+")";}else if(mode==='cot'){var rad=(unit==='deg')?v1*(Math.PI/180):v1;res=1/Math.tan(rad);formula="1 / tan("+inputDisplay+")";}var outUnit=(mode.startsWith('a')&&unit==='deg')?'°':";if(mode.startsWith('a')&&unit==='rad')outUnit=' rad';var output=""+res.toFixed(6)+outUnit+"";if(showSteps){output+="

Formula: "+formula+"";}document.getElementById('answer').innerHTML=output;}

Trig Calculator Use

This trig calculator is a comprehensive tool designed to help students, engineers, and hobbyists quickly find trigonometric ratios and their inverses. Whether you are working with right-angled triangles or periodic functions, this tool provides precise values for any angle in either degrees or radians.

Trigonometry is the branch of mathematics that studies the relationships between the side lengths and angles of triangles. By using this calculator, you can bypass manual table lookups and complex long-hand calculations, ensuring your geometry and physics problems are solved with high accuracy.

Choose a Trig Function
Select the primary function (sin, cos, tan), reciprocal function (csc, sec, cot), or inverse function (arcsin, arccos, arctan) you wish to calculate.
Angle (θ) or Value (x)
Enter the numerical value. For standard functions, this is the angle. For inverse functions, this is the ratio (typically between -1 and 1 for sine and cosine).
Unit Selection
Toggle between Degrees (0 to 360°) and Radians (0 to 2π) depending on your problem's requirements.

How the Trig Calculator Works

Trigonometry relies on the properties of a right-angled triangle. Every ratio is a comparison of two specific sides relative to a given angle θ. The primary formulas utilized by our calculator include:

sin(θ) = Opposite / Hypotenuse | cos(θ) = Adjacent / Hypotenuse | tan(θ) = Opposite / Adjacent

  • Sine: Calculates the ratio of the side opposite the angle to the hypotenuse.
  • Cosine: Calculates the ratio of the adjacent side to the hypotenuse.
  • Tangent: Calculates the ratio of the opposite side to the adjacent side.
  • Degree/Radian Conversion: The calculator internally converts degrees to radians using the formula: Radians = Degrees × (π / 180).
  • Inverse Functions: Often called "arc" functions, these allow you to find the angle when the ratio is known.

Calculation Examples

Example 1: Finding the Sine of a Standard Angle

Suppose you are building a ramp and need to find the sine of a 30-degree angle to calculate the height.

  1. Select "Sine (sin)" from the dropdown.
  2. Enter "30" in the Angle input field.
  3. Select "Degrees" as the unit.
  4. Click Calculate.
  5. Result: 0.500000

Example 2: Finding an Angle from a Ratio (Inverse)

You know that the tangent of an unknown angle is 1.0. You want to find that angle in degrees.

  1. Select "Inverse Tangent (arctan)" from the dropdown.
  2. Enter "1.0" in the Value input field.
  3. Select "Degrees" as the unit.
  4. Click Calculate.
  5. Result: 45°

Common Trigonometry Questions

What is the difference between Degrees and Radians?

Degrees are a way of measuring angles based on dividing a full circle into 360 parts. Radians are based on the radius of a circle, where a full circle is 2π radians (approx 6.28). Most engineering and physics calculations use radians, while construction and navigation often use degrees.

Why do Arcsin and Arccos have limits?

Because the sine and cosine of any angle always fall between -1 and 1, the inverse functions (arcsin and arccos) can only accept inputs within that range. If you enter a value like 2.0 into a trig calculator for arcsin, you will receive an error because no real angle has a sine greater than 1.

What is SOH CAH TOA?

It is a mnemonic device to remember the basic ratios: Sine = Opposite/Hypotenuse (SOH), Cosine = Adjacent/Hypotenuse (CAH), and Tangent = Opposite/Adjacent (TOA). This simple rule is the foundation of all right-triangle trigonometry.

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