Sin Cos Tan Calculator

Calculate all six trigonometric functions at once: sin, cos, tan, csc, sec, and cot for any angle.

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All Trigonometric Values

Trigonometric values for 45°
6 functions
sin(x)0.707107
cos(x)0.707107
tan(x)1
csc(x) = 1/sin(x)1.414214
sec(x) = 1/cos(x)1.414214
cot(x) = 1/tan(x)1
Degrees45°
Radians0.785398 rad

Step-by-Step Solution

sin²(x) + cos²(x) = 1

The Six Trigonometric Functions

In a right triangle with an angle x, the six trigonometric functions are defined as ratios of the triangle's sides. These functions are fundamental to mathematics, physics, engineering, and many other fields.

Definitions

Sine (sin)

Opposite side divided by the hypotenuse.

sin(x) = opposite / hypotenuse

Cosine (cos)

Adjacent side divided by the hypotenuse.

cos(x) = adjacent / hypotenuse

Tangent (tan)

Opposite side divided by the adjacent side.

tan(x) = opposite / adjacent

Cosecant (csc)

The reciprocal of sine.

csc(x) = 1 / sin(x)

Secant (sec)

The reciprocal of cosine.

sec(x) = 1 / cos(x)

Cotangent (cot)

The reciprocal of tangent.

cot(x) = 1 / tan(x)

Key Identities

  • Pythagorean identity: sin²(x) + cos²(x) = 1
  • tan(x) = sin(x) / cos(x)
  • 1 + tan²(x) = sec²(x)
  • 1 + cot²(x) = csc²(x)

Mnemonic: SOH CAH TOA

A popular way to remember the primary trig ratios: Sine = Opposite / Hypotenuse, Cosine = Adjacent / Hypotenuse, Tangent = Opposite / Adjacent.