Trigonometry Calculator

Calculate sine, cosine, tangent and cotangent values for any angle in degrees or radians.

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1 What are Trigonometric Functions?

2 Common Values

3 Applications

Concept

What are Trigonometric Functions?

Trigonometric functions are mathematical functions that relate the angles of a right triangle to the ratios of its sides. The main trigonometric functions are:

Basic Functions

Sine (sin): opposite/hypotenuse
Cosine (cos): adjacent/hypotenuse
Tangent (tan): opposite/adjacent
Cotangent (cot): adjacent/opposite

Properties

sin²θ + cos²θ = 1
tan θ = sin θ / cos θ
cot θ = 1 / tan θ
cot θ = cos θ / sin θ

Values

Common Values

Special Angles (Degrees)

0°: sin(0°) = 0, cos(0°) = 1, tan(0°) = 0
30°: sin(30°) = 0.5, cos(30°) = 0.866, tan(30°) = 0.577
45°: sin(45°) = 0.707, cos(45°) = 0.707, tan(45°) = 1
60°: sin(60°) = 0.866, cos(60°) = 0.5, tan(60°) = 1.732
90°: sin(90°) = 1, cos(90°) = 0, tan(90°) = undefined

Properties

sin(-θ) = -sin(θ)
cos(-θ) = cos(θ)
tan(-θ) = -tan(θ)
sin(θ + 360°) = sin(θ)
cos(θ + 360°) = cos(θ)

Applications

Applications of Trigonometric Functions

Physics Wave Motion

Trigonometric functions are used to describe wave motion, oscillations, and periodic phenomena.

Engineering Signal Processing

Trigonometric functions are fundamental in signal processing, electrical engineering, and communications.

Navigation GPS and Location

Trigonometric functions are used in navigation systems, GPS, and calculating distances and positions.

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