Find the Sin Cos Tan Calculator
Easily calculate the Sine, Cosine, and Tangent values for any angle using our free online find the sin cos tan calculator. Input your angle in degrees or radians and get instant results.
Trigonometric Calculator
Results
- If angle is in degrees, it's first converted to radians: Radians = Degrees × (π / 180)
- Sine (sin) = sin(angle in radians)
- Cosine (cos) = cos(angle in radians)
- Tangent (tan) = tan(angle in radians) = sin(angle in radians) / cos(angle in radians)
Sine and Cosine Waves (0 to 360°)
Common Angle Values
| Angle (Degrees) | Angle (Radians) | Sine (sin) | Cosine (cos) | Tangent (tan) |
|---|---|---|---|---|
| 0° | 0 | 0 | 1 | 0 |
| 30° | π/6 ≈ 0.5236 | 0.5 | √3/2 ≈ 0.8660 | 1/√3 ≈ 0.5774 |
| 45° | π/4 ≈ 0.7854 | √2/2 ≈ 0.7071 | √2/2 ≈ 0.7071 | 1 |
| 60° | π/3 ≈ 1.0472 | √3/2 ≈ 0.8660 | 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 |
What is a {primary_keyword}?
A {primary_keyword}, or trigonometric calculator, is a tool designed to compute the sine, cosine, and tangent values for a given angle. These trigonometric functions are fundamental in mathematics, physics, engineering, and various other fields, describing the relationships between the angles and sides of a right-angled triangle. Our {primary_keyword} allows you to input an angle in either degrees or radians and instantly get the sin, cos, and tan values.
Anyone studying or working with triangles, waves, oscillations, or circular motion can benefit from using a {primary_keyword}. This includes students in high school and college, engineers, architects, physicists, and even game developers. It's a handy tool for quick calculations and verifying manual work. We also provide a {related_keywords} for more general math needs.
A common misconception is that these functions are only useful for right-angled triangles. While they are defined using right-angled triangles (SOH CAH TOA), their applications extend to all triangles (using the sine and cosine rules) and periodic phenomena through their wave-like nature. The {primary_keyword} helps visualize and calculate these values regardless of the direct application.
{primary_keyword} Formula and Mathematical Explanation
The core of a {primary_keyword} lies in the trigonometric functions sine (sin), cosine (cos), and tangent (tan). For an angle θ within a right-angled triangle:
- Sine (θ) = Opposite / Hypotenuse
- Cosine (θ) = Adjacent / Hypotenuse
- Tangent (θ) = Opposite / Adjacent
When dealing with angles beyond those in a simple right-angled triangle, we often use the unit circle (a circle with a radius of 1 centered at the origin of a Cartesian plane). For an angle θ measured counter-clockwise from the positive x-axis, a point (x, y) on the unit circle corresponding to that angle will have coordinates x = cos(θ) and y = sin(θ). Tangent is then tan(θ) = y/x = sin(θ)/cos(θ).
Our {primary_keyword} first converts the input angle to radians if it's given in degrees, as the standard mathematical functions in most programming languages (including JavaScript used here) expect angles in radians.
Conversion: Radians = Degrees × (π / 180)
Then, it calculates:
- sin(θ) = Math.sin(angle in radians)
- cos(θ) = Math.cos(angle in radians)
- tan(θ) = Math.tan(angle in radians) (undefined when cos(θ) = 0, i.e., at 90°, 270°, etc.)
The {primary_keyword} handles these calculations for you.
Variables Table
| Variable | Meaning | Unit | Typical Range |
|---|---|---|---|
| θ (Angle) | The input angle | Degrees or Radians | 0-360 degrees or 0-2π radians (though can be any real number) |
| sin(θ) | Sine of the angle | Dimensionless | -1 to 1 |
| cos(θ) | Cosine of the angle | Dimensionless | -1 to 1 |
| tan(θ) | Tangent of the angle | Dimensionless | -∞ to ∞ (undefined at odd multiples of 90° or π/2) |
Practical Examples (Real-World Use Cases)
Let's see how to use the {primary_keyword} with some examples.
Example 1: Finding the height of a tree
You are standing 20 meters away from a tree and measure the angle of elevation to the top of the tree as 35 degrees. You want to find the height of the tree. The height (opposite) is related to the distance (adjacent) by the tangent function: tan(35°) = Height / 20m.
Using the {primary_keyword}:
- Enter 35 into the "Angle Value" field.
- Select "Degrees".
- The calculator shows tan(35°) ≈ 0.7002.
So, Height = 20m * 0.7002 ≈ 14 meters. The tree is approximately 14 meters tall.
Example 2: Analyzing an AC circuit
In an alternating current (AC) circuit, the voltage might be described by V(t) = V₀ sin(ωt + φ). If ωt + φ = π/3 radians (or 60 degrees) at a certain time, you might want to find the instantaneous voltage relative to the peak voltage V₀. You need sin(π/3).
Using the {primary_keyword}:
- Enter 60 (or approximately 1.0472 if using radians) into the "Angle Value" field.
- Select "Degrees" (or "Radians" if you entered 1.0472).
- The calculator shows sin(60°) ≈ 0.866.
So, the instantaneous voltage is about 0.866 times the peak voltage at that moment.
For more detailed calculations, you might explore our {related_keywords}.
How to Use This {primary_keyword} Calculator
Using our {primary_keyword} is straightforward:
- Enter the Angle Value: Type the numerical value of the angle into the "Angle Value" input field.
- Select the Unit: Choose whether the angle you entered is in "Degrees" or "Radians" using the radio buttons.
- View Results: The calculator automatically updates and displays the Sine, Cosine, and Tangent values for your angle in the "Results" section as you type or change the unit. If not, click "Calculate".
- Interpret Results: The "Results" section shows the angle in both degrees and radians, and the calculated sin, cos, and tan values. The "Primary Result" gives a quick summary.
- Reset: Click the "Reset" button to clear the input and results to their default values (30 degrees).
- Copy Results: Click "Copy Results" to copy the angle (both units), sin, cos, and tan values to your clipboard.
The chart below the calculator visualizes the sine and cosine values for angles from 0 to 360 degrees, with your entered angle highlighted, helping you understand the periodic nature of these functions.
Key Factors That Affect {primary_keyword} Results
The results from a {primary_keyword} are directly and solely dependent on two factors:
- The Angle Value: The numerical value of the angle is the primary input. Different angles yield different sin, cos, and tan values.
- The Angle Unit: Whether the angle is interpreted as degrees or radians is crucial. 30 degrees is very different from 30 radians. Ensure you select the correct unit.
- Precision of π: The conversion between degrees and radians uses the value of π. Our calculator uses the `Math.PI` constant for high precision.
- Calculator's Internal Precision: The underlying floating-point arithmetic of the system running the {primary_keyword} can introduce very minor rounding differences at extreme precision levels, but for most practical purposes, these are negligible.
- Tangent at 90°, 270°, etc.: The tangent function is undefined at 90° (π/2 radians), 270° (3π/2 radians), and other odd multiples of 90° because the cosine is zero at these angles, leading to division by zero. Our calculator will show "Undefined" or a very large number approaching infinity.
- Input Validity: The {primary_keyword} expects a numerical input for the angle. Non-numerical inputs will result in errors.
Understanding these factors ensures you use the {primary_keyword} correctly and interpret the results accurately. If you are working with complex numbers, our {related_keywords} might be useful.
Frequently Asked Questions (FAQ)
- Q1: What are sine, cosine, and tangent?
- A1: Sine (sin), cosine (cos), and tangent (tan) are the primary trigonometric functions that relate the angles of a right-angled triangle to the ratios of its sides. They are also used to describe periodic phenomena.
- Q2: How do I switch between degrees and radians in the {primary_keyword}?
- A2: Simply select the "Degrees" or "Radians" radio button next to the angle input field before or after entering the angle value.
- Q3: Why does the tangent become "Undefined" or very large?
- A3: Tangent is calculated as sin/cos. When the angle is 90°, 270°, or any odd multiple of 90°, the cosine is 0. Division by zero is undefined, so the tangent is undefined at these points.
- Q4: Can I enter negative angles in the {primary_keyword}?
- A4: Yes, the {primary_keyword} accepts negative angle values. sin(-x) = -sin(x), cos(-x) = cos(x), tan(-x) = -tan(x).
- Q5: What is the range of values for sin, cos, and tan?
- A5: Sine and cosine values range from -1 to 1, inclusive. Tangent values can range from negative infinity to positive infinity.
- Q6: How accurate is this {primary_keyword}?
- A6: Our {primary_keyword} uses standard JavaScript `Math` functions, which provide high precision for trigonometric calculations, typically accurate to about 15-17 decimal places within the limits of standard floating-point numbers.
- Q7: Can I use this {primary_keyword} for angles greater than 360 degrees or 2π radians?
- A7: Yes, you can enter any real number as the angle. The trigonometric functions are periodic, so sin(θ + 360°) = sin(θ), cos(θ + 360°) = cos(θ), etc. (or θ + 2π for radians).
- Q8: What are the inverse functions (arcsin, arccos, arctan)?
- A8: Inverse trigonometric functions (like arcsin, arccos, arctan) are used to find the angle when you know the value of the sine, cosine, or tangent. This calculator focuses on finding sin, cos, and tan from the angle. We also have a {related_keywords} that might help with inverse functions.
Related Tools and Internal Resources
- {related_keywords}: Explore our general math calculator for various calculations.
- {related_keywords}: Calculate areas and perimeters of various geometric shapes.
- {related_keywords}: If you're working with vectors, this tool might be helpful.
- {related_keywords}: Another useful tool for mathematical operations.
- {related_keywords}: For statistical calculations.
- {related_keywords}: More advanced math tools.