Examples for

Trigonometry

Trigonometry is the study of the relationships between side lengths and angles of triangles and the applications of these relationships. The field is fundamental to mathematics, engineering and a wide variety of sciences. Wolfram|Alpha has comprehensive functionality in the area and is able to compute values of trigonometric functions, solve equations involving trigonometry and more.

Trigonometric Calculations

Evaluate trigonometric functions or larger expressions involving trigonometric functions with different input values.

Compute values of trigonometric functions:

sin(pi/5)
tan(60 deg)

Compute values of inverse trigonometric functions:

arcsin(1/2)

Trigonometric Identities

Learn about and apply well-known trigonometric identities.

Find multiple-angle formulas:

expand sin 4x

Find addition formulas:

expand sin(x+y+z)

Find other trig identities:

factor sin x + sin y

Spherical Trigonometry

Study the relationships between side lengths and angles of triangles when these triangles are drawn atop a spherical surface.

Apply a theorem of spherical trigonometry:

law of haversines

Trigonometric Functions

Learn about and perform computations using trigonometric functions and their inverses, over the real or complex numbers.

Compute properties of a trigonometric function:

cos x
sec(5x)

Compute properties of an inverse trigonometric function:

arccot x

Plot a trigonometric function:

plot sin(x)

Analyze a trigonometric function of a complex variable:

sin(z)

Analyze a trigonometric polynomial:

cos(x) + 1/2 cos(2x) + 1/4 cos(4x)

Generate a table of special values of a function:

closed-form values of tan(x)

Compute the root mean square of a periodic function:

root mean square 3sin(t)-2cos(2t)
root mean square squarewave(t/3) + sin(pi t)

Trigonometric Equations

Solve equations involving trigonometric functions.

Solve a trigonometric equation:

sin x + cos x = 1

GO FURTHER

Step-by-Step Solutions for Proofs

RELATED EXAMPLES

  • Algebra
  • Applied Mathematics
  • Calculus & Analysis
  • Complex Analysis
  • Geometry
  • Oscillations & Waves
  • Periodic Functions

    • Trigonometric Theorems

    Learn about and apply well-known trigonometric theorems.

    Apply a trigonometric theorem:

    law of cosines
    law of sines a=6cm, b=8cm, alpha=40deg

    Apply the Pythagorean theorem:

    Pythagorean theorem a=10, b=24