Trigonometry Calculator

Trigonometry Calculator

Trigonometric Functions

Results:

Function Value: -
Angle in Degrees: -
Angle in Radians: -

Right Triangle Calculator

Results:

Hypotenuse: -
Opposite: -
Adjacent: -
Angle (θ): -

Graphical Interpretation

Trigonometric Formulas

Basic Trigonometric Ratios

  • Sine (sin): Opposite / Hypotenuse
  • Cosine (cos): Adjacent / Hypotenuse
  • Tangent (tan): Opposite / Adjacent
  • Cosecant (csc): Hypotenuse / Opposite
  • Secant (sec): Hypotenuse / Adjacent
  • Cotangent (cot): Adjacent / Opposite

Inverse Trigonometric Functions

  • Arcsine: sin⁻¹x
  • Arccosine: cos⁻¹x
  • Arctangent: tan⁻¹x
  • Arccotangent: cot⁻¹x
  • Arcsecant: sec⁻¹x
  • Arccosecant: csc⁻¹x

Summary of Trigonometric Functions

Function Description Relationship (radians) Relationship (degrees)
sine opposite / hypotenuse sinθ = cos(π/2 - θ) = 1/cscθ sinx = cos(90° - x) = 1/cscx
cosine adjacent / hypotenuse cosθ = sin(π/2 - θ) = 1/secθ cosx = sin(90° - x) = 1/secx
tangent opposite / adjacent tanθ = sinθ/cosθ = cot(π/2 - θ) = 1/cotθ tanx = sinx/cosx = cot(90° - x) = 1/cotx
cotangent adjacent / opposite cotθ = cosθ/sinθ = tan(π/2 - θ) = 1/tanθ cotx = cosx/sinx = tan(90° - x) = 1/tanx
secant hypotenuse / adjacent secθ = csc(π/2 - θ) = 1/cosθ secx = csc(90° - x) = 1/cosx
cosecant hypotenuse / opposite cscθ = sec(π/2 - θ) = 1/sinθ cscx = sec(90° - x) = 1/sinx

What is Trigonometry and Trigonometric Ratios?

The study of the angles of a triangle is called trigonometry. This calculator determines all interconnected angle ratios efficiently.

Practical Example

Find the value of each trigonometric ratio for a triangle with:

  • Opposite = 4
  • Adjacent = 3
  • Hypotenuse = 5

Results would be:

  • Sine(θ) = 0.8
  • Cosine(θ) = 0.6
  • Tangent(θ) = 1.33
  • Secant(θ) = 1.25
  • Cosecant(θ) = 1.67
  • Cotangent(θ) = 0.75

Trigonometric Formulas

Basic Trigonometric Ratios

  • Sine (sin): Opposite / Hypotenuse
  • Cosine (cos): Adjacent / Hypotenuse
  • Tangent (tan): Opposite / Adjacent
  • Cosecant (csc): Hypotenuse / Opposite
  • Secant (sec): Hypotenuse / Adjacent
  • Cotangent (cot): Adjacent / Opposite

Inverse Trigonometric Functions

  • Arcsine: sin⁻¹x
  • Arccosine: cos⁻¹x
  • Arctangent: tan⁻¹x
  • Arccotangent: cot⁻¹x
  • Arcsecant: sec⁻¹x
  • Arccosecant: csc⁻¹x

Summary of Trigonometric Functions

Function Description Relationship (radians) Relationship (degrees)
sine opposite / hypotenuse sinθ = cos(π/2 - θ) = 1/cscθ sinx = cos(90° - x) = 1/cscx
cosine adjacent / hypotenuse cosθ = sin(π/2 - θ) = 1/secθ cosx = sin(90° - x) = 1/secx
tangent opposite / adjacent tanθ = sinθ/cosθ = cot(π/2 - θ) = 1/cotθ tanx = sinx/cosx = cot(90° - x) = 1/cotx
cotangent adjacent / opposite cotθ = cosθ/sinθ = tan(π/2 - θ) = 1/tanθ cotx = cosx/sinx = tan(90° - x) = 1/tanx
secant hypotenuse / adjacent secθ = csc(π/2 - θ) = 1/cosθ secx = csc(90° - x) = 1/cosx
cosecant hypotenuse / opposite cscθ = sec(π/2 - θ) = 1/sinθ cscx = sec(90° - x) = 1/sinx

What is Trigonometry and Trigonometric Ratios?

The study of the angles of a triangle is called trigonometry. This calculator determines all interconnected angle ratios efficiently.

Practical Example

Find the value of each trigonometric ratio for a triangle with:

  • Opposite = 4
  • Adjacent = 3
  • Hypotenuse = 5

Results would be:

  • Sine(θ) = 0.8
  • Cosine(θ) = 0.6
  • Tangent(θ) = 1.33
  • Secant(θ) = 1.25
  • Cosecant(θ) = 1.67
  • Cotangent(θ) = 0.75