Find Sin Cos Tan Calculator

Easily calculate the sine, cosine, and tangent of any angle with our free online Sin Cos Tan Calculator. Input your angle in degrees or radians and get instant results.

Trigonometric Function Calculator

Common Trigonometric Values

Angle (Degrees)	Angle (Radians)	sin(θ)	cos(θ)	tan(θ)
0°	0	0	1	0
30°	π/6 (≈0.5236)	1/2 (0.5)	√3/2 (≈0.8660)	1/√3 (≈0.5774)
45°	π/4 (≈0.7854)	1/√2 (≈0.7071)	1/√2 (≈0.7071)	1
60°	π/3 (≈1.0472)	√3/2 (≈0.8660)	1/2 (0.5)	√3 (≈1.7321)
90°	π/2 (≈1.5708)	1	0	Undefined
180°	π (≈3.1416)	0	-1	0
270°	3π/2 (≈4.7124)	-1	0	Undefined
360°	2π (≈6.2832)	0	1	0

Table of sine, cosine, and tangent values for common angles.

What is a Sin Cos Tan Calculator?

A Sin Cos Tan Calculator is a tool used to determine the trigonometric ratios – sine (sin), cosine (cos), and tangent (tan) – for a given angle. These ratios are fundamental in trigonometry, a branch of mathematics that studies relationships involving lengths and angles of triangles. The calculator typically takes an angle as input, either in degrees or radians, and outputs the values of sin, cos, and tan for that angle.

This calculator is essential for students studying mathematics (especially trigonometry, geometry, and calculus), engineers, physicists, architects, and anyone working with angles and their relationships in right-angled triangles or periodic phenomena like waves.

Common misconceptions include thinking that sin, cos, and tan are lengths themselves; they are actually ratios of lengths of sides in a right-angled triangle relative to one of its acute angles, or coordinates on the unit circle.

Sin Cos Tan Formulas and Mathematical Explanation

The trigonometric functions sine, cosine, and tangent are defined based on the ratios of the sides of a right-angled triangle with respect to one of its acute angles (let's call it θ):

• Sine (sin θ) = Length of the side Opposite to angle θ / Length of the Hypotenuse
• Cosine (cos θ) = Length of the side Adjacent to angle θ / Length of the Hypotenuse
• Tangent (tan θ) = Length of the side Opposite to angle θ / Length of the side Adjacent to angle θ

Also, tan θ can be expressed as sin θ / cos θ.

When using a Sin Cos Tan Calculator, if the angle is provided in degrees, it is first converted to radians before being used in the standard trigonometric functions (like those in JavaScript's `Math` object), because these functions typically expect angles in radians. The conversion is: Radians = Degrees × (π / 180).

Variables Table

Variable	Meaning	Unit	Typical Range
θ (Angle)	The input angle	Degrees or Radians	Any real number (though often 0-360° or 0-2π rad)
sin(θ)	Sine of the angle	Dimensionless ratio	-1 to 1
cos(θ)	Cosine of the angle	Dimensionless ratio	-1 to 1
tan(θ)	Tangent of the angle	Dimensionless ratio	-∞ to ∞ (undefined at 90°, 270°, etc.)

Practical Examples (Real-World Use Cases)

The Sin Cos Tan Calculator is invaluable in many real-world scenarios:

Example 1: Finding the Height of a Building

Imagine you are standing 50 meters away from the base of a building, and you measure the angle of elevation to the top of the building as 30 degrees. You can use the tangent function to find the height (h) of the building.

tan(30°) = Opposite / Adjacent = h / 50 meters
h = 50 * tan(30°)
Using a Sin Cos Tan Calculator, tan(30°) ≈ 0.5774.
So, h = 50 * 0.5774 ≈ 28.87 meters.

Example 2: Analyzing Wave Phenomena

In physics, sine and cosine functions are used to describe oscillations and waves, like sound waves or alternating current (AC). An AC voltage might be described by V(t) = V_max * sin(ωt), where t is time, ω is angular frequency, and V_max is the peak voltage. A Sin Cos Tan Calculator helps evaluate the voltage at any given time if the phase angle ωt is known.

How to Use This Sin Cos Tan Calculator

1. Enter the Angle: Type the value of the angle into the "Angle Value" input field.
2. Select the Unit: Choose whether the angle you entered is in "Degrees (°)" or "Radians (rad)" by clicking the corresponding radio button.
3. View Results: The calculator automatically updates and displays the sine, cosine, and tangent of the angle, as well as the angle converted to the other unit. The primary result (sine) is highlighted.
4. Understand Formulas: The "Formula-explanation" section shows the basic definitions and unit conversion if applicable.
5. Reset: Click the "Reset" button to return the angle to 30 degrees and the unit to degrees.
6. Copy Results: Click "Copy Results" to copy the main result, intermediate values, and the angle in both units to your clipboard.

The results from the Sin Cos Tan Calculator give you the fundamental trigonometric ratios for the input angle.

Key Factors That Affect Sin Cos Tan Results

• Angle Value: The primary input; the values of sin, cos, and tan directly depend on the angle's magnitude.
• Angle Unit (Degrees or Radians): It is crucial to specify the correct unit. Calculators and programming functions often default to radians, so conversion from degrees (multiplying by π/180) is essential if the input is in degrees. Our Sin Cos Tan Calculator handles this.
• Calculator Precision: The number of decimal places the calculator uses can affect the precision of the results. Most calculators provide high precision.
• Quadrant of the Angle: The signs (+ or -) of sin, cos, and tan depend on which quadrant (0-90°, 90-180°, 180-270°, 270-360°) the angle lies in.
• Special Angles: For angles like 0°, 30°, 45°, 60°, 90°, etc., the sin, cos, and tan values are often exact fractions or involve square roots, but are displayed as decimals by the calculator.
• Undefined Values: Tangent is undefined for angles like 90°, 270°, and their co-terminal angles, as cos is zero at these points, leading to division by zero. A good Sin Cos Tan Calculator might indicate "Undefined" or a very large number.

Frequently Asked Questions (FAQ)

1. What are sine, cosine, and tangent? They are the primary trigonometric ratios relating the angles of a right-angled triangle to the lengths of its sides. They can also be defined using the unit circle.

2. What is the difference between degrees and radians? Degrees and radians are two different units for measuring angles. A full circle is 360 degrees or 2π radians. 180 degrees = π radians. Most mathematical software uses radians.

3. Why is tan(90°) undefined? Tan(θ) = sin(θ) / cos(θ). At 90°, cos(90°) = 0. Division by zero is undefined.

4. What is the range of sin and cos values? Both sine and cosine values range from -1 to +1, inclusive.

5. What is the range of tan values? Tangent values can range from negative infinity to positive infinity.

6. How do I convert degrees to radians? Multiply the angle in degrees by π/180. Our Sin Cos Tan Calculator does this automatically if you input in degrees.

7. Can I use this calculator for angles greater than 360° or negative angles? Yes, trigonometric functions are periodic. For example, sin(390°) = sin(390° – 360°) = sin(30°). The calculator handles these.

8. Where are trigonometric functions used? They are used in physics (waves, optics, mechanics), engineering, navigation, computer graphics, architecture, and many other fields. Using a Sin Cos Tan Calculator simplifies these applications.

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