Understanding Trigonometric Functions

Trigonometric functions (sine, cosine, tangent) relate angles of a triangle to ratios of its sides. These functions are fundamental in geometry, physics, engineering, and many scientific fields.

How to Use This Calculator

Enter an angle value in the input field
Select whether your angle is in degrees or radians
Choose your desired decimal precision
Click "Calculate" to see all three trigonometric values

Common Reference Values

Angle	sin(θ)	cos(θ)	tan(θ)
0°	0	1	0
30°	1/2	√3/2	√3/3
45°	√2/2	√2/2	1
60°	√3/2	1/2	√3
90°	1	0	undefined

Important Notes

Tangent is undefined at 90° and 270° (π/2 and 3π/2 radians)
Values repeat every 360° (2π radians) due to periodicity
For angles beyond 90°, consider reference angles in other quadrants
This calculator uses JavaScript's built-in Math functions for computation

Frequently Asked Questions

What's the difference between degrees and radians?

Degrees divide a circle into 360 equal parts, while radians are based on the radius of the circle (2π radians = 360°). Radians are the standard unit in higher mathematics.

Why is tangent undefined at 90°?

Tangent = sine/cosine. At 90°, cosine = 0, making the division by zero mathematically undefined.

How are values calculated for angles beyond 90°?

The calculator uses periodicity and trigonometric identities to find equivalent values in the first quadrant (0-90°).

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