Trigonometric Functions Calculator

Trigonometry is a branch of mathematics that studies the relationships between the sides and angles of triangles. It defines six fundamental functions — sine, cosine, tangent, cosecant, secant, and cotangent — that describe these relationships. Trigonometry is foundational to geometry, physics, engineering, and many other fields.

The six trig functions are sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), and cotangent (cot). Cosecant is the reciprocal of sine, secant is the reciprocal of cosine, and cotangent is the reciprocal of tangent. Together they fully describe the angular relationships in a triangle or unit circle.

To convert degrees to radians, multiply the angle in degrees by π/180. For example, 90° × (π/180) = π/2 radians ≈ 1.5708 rad. This calculator accepts both degrees and radians so you don't need to convert manually — just select the appropriate unit.

Take the decimal part of the degree value and multiply it by 60 to get minutes, then take the decimal part of the minutes and multiply by 60 to get seconds. For example, 45.75° = 45° 45' 0". Most scientific calculators and this tool accept decimal degrees directly.

Trigonometry is used in a wide range of real-world applications including architecture, engineering, physics, astronomy, navigation, and computer graphics. It's essential for calculating distances, heights, wave patterns, signal processing, and rotations in 3D space.

Certain trig functions are undefined at specific angles because they involve division by zero. For example, tan(90°) is undefined because cos(90°) = 0, and tan = sin/cos. Similarly, csc is undefined at 0° and 180° because sin = 0 at those angles. This calculator will display 'undefined' in those cases.

Trigonometry has ancient roots dating back to Egyptian and Babylonian mathematics. The Greek astronomer Hipparchus (around 190–120 BC) is often credited as the father of trigonometry for creating the first known trigonometric table. Indian mathematicians later developed the modern sine and cosine functions.

Trigonometry is usually introduced in high school, typically around grades 10–11 (ages 15–17), often as part of a precalculus or advanced algebra course. It is further developed in calculus and college-level mathematics courses.