Free online trigonometry calculators for unit circle values, sine, cosine, tangent, and other trigonometric functions. Calculate angles, radians, and trigonometric identities step-by-step.
Trigonometry is a fundamental branch of mathematics that deals with the relationships between angles and sides of triangles. Our comprehensive trigonometry calculator suite provides tools for calculating essential trigonometric functions including sine, cosine, tangent, secant, cosecant, and cotangent. Whether you're a student learning trigonometry basics, an engineer solving complex problems, or preparing for exams, our calculator offers accurate results with detailed explanations.
This trigonometry toolset helps visualize concepts using the unit circle, converts between radians and degrees, and solves trigonometric equations. Each function includes step-by-step solutions to enhance your understanding of fundamental trigonometric principles.
Enter the angle value you want to calculate
Enter an angle to calculate
For 30° (π/6): sin(30°) = 1/2, cos(30°) = √3/2, tan(30°) = √3/3
In a right triangle with angle A = 45° and hypotenuse = 10, opposite side = 10×sin(45°) = 10×(√2/2) ≈ 7.07
Converting 45° to radians: 45° × (π/180°) = π/4 radians ≈ 0.785 radians
Verifying sin²(x) + cos²(x) = 1 for x = 60°: (√3/2)² + (1/2)² = 3/4 + 1/4 = 1
Students learning trigonometric concepts and solving homework problems
Calculating forces, waveforms, and angular relationships in design
Determining angles, slopes, and structural measurements
Trigonometric functions relate angles in a right triangle to the ratios of sides. The primary functions are sine (opposite/hypotenuse), cosine (adjacent/hypotenuse), and tangent (opposite/adjacent). These functions can be extended to all real numbers using the unit circle.
The unit circle is a circle with radius 1 centered at the origin of a coordinate system. It provides a way to define trigonometric functions for all angles (not just acute angles in right triangles). For any angle θ, the coordinates (cos θ, sin θ) lie on the unit circle.
Degrees and radians are two units for measuring angles. A full circle is 360° or 2π radians. Radians are often preferred in higher mathematics because they simplify many formulas. The conversion formula is: radians = degrees × π/180°.
These are equations involving trigonometric functions that are true for all values where both sides are defined. Key identities include the Pythagorean identity (sin²θ + cos²θ = 1), sum and difference formulas, and double-angle formulas.
The unit circle provides a geometric way to define trigonometric functions for all angles. It helps visualize the values of sine and cosine for any angle and demonstrates the periodic nature of these functions. The unit circle also helps understand the relationship between angles in different quadrants.
Degrees are commonly used in geometry problems and everyday applications. Radians are preferred in calculus and higher mathematics because they simplify many formulas and derivative relationships. Angular velocity and frequency problems often use radians.
Trigonometric ratios are defined for acute angles in right triangles, while trigonometric functions extend these definitions to all real numbers using the unit circle. Functions can have negative values and work for angles greater than 90°.
The four quadrants allow trigonometric functions to have both positive and negative values, which is essential for modeling oscillating phenomena like sound waves, electrical currents, and harmonic motion. Each quadrant has different sign combinations for sine and cosine.
Focus on the first quadrant angles (0°, 30°, 45°, 60°, 90°) and memorize the sine values: 0, 1/2, √2/2, √3/2, 1. The cosine values are in reverse order. For other quadrants, use reference angles and adjust signs according to the ASTC rule.
Yes, this calculator provides the foundational understanding needed for advanced mathematics including calculus, differential equations, and Fourier analysis. The step-by-step solutions help reinforce concepts needed in higher-level math courses.