Sin / Cos / Tan Calculator
Enter an angle above.
Inverse Trig Calculator
Find the angle from a ratio value (−1 to 1 for sin/cos, any for tan)
Value must be between −1 and 1 for arcsin/arccos.
Sine, Cosine and Tangent Explained
Sin, cos and tan are the three primary trigonometric functions. They relate the angles of a right triangle to the ratios of its sides.
- sin(θ) = opposite ÷ hypotenuse
- cos(θ) = adjacent ÷ hypotenuse
- tan(θ) = opposite ÷ adjacent = sin(θ) ÷ cos(θ)
The Reciprocal Functions
- csc(θ) = 1 / sin(θ) (cosecant)
- sec(θ) = 1 / cos(θ) (secant)
- cot(θ) = cos(θ) / sin(θ) (cotangent)
Pythagorean Identity
The most important trig identity: sin²(θ) + cos²(θ) = 1. This holds for all angles and follows directly from the Pythagorean theorem applied to the unit circle.
Frequently Asked Questions
What does arcsin mean?
arcsin (or sin⁻¹) is the inverse sine function. It takes a ratio between −1 and 1 and returns the angle whose sine equals that ratio. For example, arcsin(0.5) = 30°.
Why do sin and cos oscillate between -1 and 1?
On the unit circle (radius = 1), sin(θ) is the y-coordinate and cos(θ) is the x-coordinate of a point on the circle. Since both coordinates must lie within the circle, they are always bounded by −1 and 1.
In which fields is trigonometry used?
Trigonometry is foundational in architecture (roof pitch, structural angles), physics (wave mechanics, optics), astronomy (parallax, orbital calculations), computer graphics (3D rotations), signal processing, and electrical engineering (AC circuit analysis).