Trigonometric Function Calculator Degrees

This trigonometric function calculator computes sine, cosine, and tangent values for angles measured in degrees. The calculator provides precise results and includes a visualization of the trigonometric functions.

How to Use This Calculator

To calculate trigonometric functions in degrees:

Enter the angle in degrees in the input field.
Select the trigonometric function you want to calculate (sine, cosine, or tangent).
Click the "Calculate" button to see the result.
The calculator will display the result and update the chart visualization.

The calculator provides results with up to 10 decimal places for precision. The chart shows the selected trigonometric function over a range of angles centered around your input angle.

Formula Explained

Trigonometric Functions in Degrees

The trigonometric functions sine, cosine, and tangent are defined as ratios of sides in a right-angled triangle. For an angle θ in degrees:

Sine (sin θ) = Opposite side / Hypotenuse
Cosine (cos θ) = Adjacent side / Hypotenuse
Tangent (tan θ) = Opposite side / Adjacent side

These functions can be calculated using the following formulas:

sin θ = sin(θ × π/180)
cos θ = cos(θ × π/180)
tan θ = tan(θ × π/180)

Where θ is the angle in degrees, and π/180 is the conversion factor to radians.

The calculator uses JavaScript's built-in Math.sin(), Math.cos(), and Math.tan() functions, which expect angles in radians. The calculator converts the input angle from degrees to radians before performing the calculation.

Worked Examples

Example 1: Calculating sin(30°)

To calculate sin(30°):

Enter 30 in the angle input field.
Select "Sine" from the function dropdown.
Click "Calculate".

The calculator will display: sin(30°) = 0.5000000000

This is because sin(30°) is a standard trigonometric value that equals 0.5.

Example 2: Calculating cos(45°)

To calculate cos(45°):

Enter 45 in the angle input field.
Select "Cosine" from the function dropdown.
Click "Calculate".

The calculator will display: cos(45°) = 0.7071067812

This is because cos(45°) is approximately 0.7071.

Example 3: Calculating tan(60°)

To calculate tan(60°):

Enter 60 in the angle input field.
Select "Tangent" from the function dropdown.
Click "Calculate".

The calculator will display: tan(60°) = 1.7320508076

This is because tan(60°) is approximately 1.7321.

Frequently Asked Questions

What is the difference between degrees and radians?: A full circle is 360 degrees or 2π radians. Degrees are commonly used in everyday applications, while radians are more common in advanced mathematics and physics.
Why does the calculator show different results for the same angle?: The calculator shows different results based on the selected trigonometric function (sine, cosine, or tangent). Each function provides a different ratio of sides in a right-angled triangle.
How accurate are the results from this calculator?: The calculator provides results with up to 10 decimal places, which is highly accurate for most practical applications. The results are calculated using JavaScript's built-in Math functions.
Can I use this calculator for angles greater than 360 degrees?: Yes, you can enter any angle value, and the calculator will compute the trigonometric function correctly. The calculator uses the modulo operation to handle angles outside the standard 0-360 degree range.
What is the difference between sine and cosine?: Sine and cosine are both trigonometric functions that relate the angles of a right triangle to the ratios of its sides. Sine is the ratio of the opposite side to the hypotenuse, while cosine is the ratio of the adjacent side to the hypotenuse.