Sine Cosine Tangent Calculator

Sine, Cosine, Tangent Calculator

function calculateTrigFunctions() { var angleValue = parseFloat(document.getElementById('angleValue').value); var angleUnit = document.getElementById('angleUnit').value; if (isNaN(angleValue)) { document.getElementById('resultSine').textContent = 'Please enter a valid number.'; document.getElementById('resultCosine').textContent = "; document.getElementById('resultTangent').textContent = "; return; } var angleInRadians; if (angleUnit === 'degrees') { angleInRadians = angleValue * (Math.PI / 180); } else { angleInRadians = angleValue; } var sineResult = Math.sin(angleInRadians); var cosineResult = Math.cos(angleInRadians); var tangentResult; // Check for tangent undefined cases (e.g., 90, 270 degrees) // Normalize angle to be within 0 to 2*PI for consistent checking var normalizedAngle = angleInRadians % (2 * Math.PI); if (normalizedAngle < 0) { normalizedAngle += 2 * Math.PI; } // Check if angle is close to PI/2 or 3*PI/2 (90 or 270 degrees) // Use a small epsilon for floating point comparison var epsilon = 1e-9; if (Math.abs(normalizedAngle – Math.PI / 2) < epsilon || Math.abs(normalizedAngle – 3 * Math.PI / 2) < epsilon) { tangentResult = 'Undefined'; } else { tangentResult = Math.tan(angleInRadians); } document.getElementById('resultSine').textContent = sineResult.toFixed(6); document.getElementById('resultCosine').textContent = cosineResult.toFixed(6); document.getElementById('resultTangent').textContent = (typeof tangentResult === 'number') ? tangentResult.toFixed(6) : tangentResult; }

Understanding Sine, Cosine, and Tangent in Trigonometry

Sine, Cosine, and Tangent are fundamental trigonometric ratios that describe the relationships between the angles and sides of a right-angled triangle. These functions are crucial in various fields, including mathematics, physics, engineering, and computer graphics, for analyzing periodic phenomena, calculating distances, and modeling waves.

What are Sine, Cosine, and Tangent?

Consider a right-angled triangle with an angle θ (theta). The sides of the triangle relative to this angle are:

• Opposite: The side directly across from angle θ.
• Adjacent: The side next to angle θ that is not the hypotenuse.
• Hypotenuse: The longest side, opposite the right angle.

The trigonometric ratios are defined as follows:

• Sine (sin θ): The ratio of the length of the opposite side to the length of the hypotenuse.
  sin θ = Opposite / Hypotenuse
• Cosine (cos θ): The ratio of the length of the adjacent side to the length of the hypotenuse.
  cos θ = Adjacent / Hypotenuse
• Tangent (tan θ): The ratio of the length of the opposite side to the length of the adjacent side. It can also be expressed as sin θ / cos θ.
  tan θ = Opposite / Adjacent

How to Use the Sine, Cosine, Tangent Calculator

Our calculator simplifies the process of finding these trigonometric values for any given angle. Follow these steps:

1. Enter Angle Value: Input the numerical value of the angle you wish to calculate. For example, you might enter '30', '45', '90', or '1.57'.
2. Select Angle Unit: Choose whether your angle is in 'Degrees' or 'Radians' from the dropdown menu. It's crucial to select the correct unit for accurate results.
3. Click 'Calculate': Press the "Calculate" button to instantly see the sine, cosine, and tangent values for your specified angle.

Examples of Use:

• Example 1: Angle of 30 Degrees

  If you input 30 and select Degrees:

  • Sine (30°) ≈ 0.500000
  • Cosine (30°) ≈ 0.866025
  • Tangent (30°) ≈ 0.577350
• Example 2: Angle of 45 Degrees

  If you input 45 and select Degrees:

  • Sine (45°) ≈ 0.707107
  • Cosine (45°) ≈ 0.707107
  • Tangent (45°) ≈ 1.000000
• Example 3: Angle of 90 Degrees

  If you input 90 and select Degrees:

  • Sine (90°) = 1.000000
  • Cosine (90°) = 0.000000
  • Tangent (90°) = Undefined (because cos 90° is 0, and division by zero is undefined)
• Example 4: Angle of π/2 Radians

  If you input 1.570796 (approx. π/2) and select Radians:

  • Sine (π/2 rad) ≈ 1.000000
  • Cosine (π/2 rad) ≈ 0.000000
  • Tangent (π/2 rad) = Undefined

Applications of Trigonometric Functions

Trigonometric functions are indispensable in many areas:

• Physics: Describing wave motion, oscillations, projectile motion, and analyzing forces.
• Engineering: Designing structures, analyzing electrical circuits (AC current), and in signal processing.
• Navigation: Calculating distances and directions in air and sea travel.
• Astronomy: Determining positions of celestial bodies and distances in space.
• Computer Graphics: Creating realistic 3D models, animations, and game development.

Whether you're a student learning trigonometry, an engineer designing a bridge, or a physicist modeling a wave, this calculator provides a quick and accurate way to find the sine, cosine, and tangent of any angle.