Sine, Cosine, Tangent Calculator
Compute sine (sin), cosine (cos), and tangent (tan) for any angle in degrees. Free online trigonometry calculator with interactive graphs for students and professionals.
About This Calculator
Our Sine, Cosine, Tangent Calculator computes the three primary trigonometric functions for any angle in degrees. Whether you're a student learning trigonometry basics, an engineer solving angles in structural designs, or a professional physicist working with wave functions, this free online tool provides instant sin(θ), cos(θ), and tan(θ) values with up to six decimal precision. The interactive chart lets you visualize how each trigonometric function behaves across the full 0 deg to 360 deg cycle, revealing important periodic patterns and relationships.
Sine, cosine, and tangent are defined from a right triangle: sin(θ) = opposite/hypotenuse, cos(θ) = adjacent/hypotenuse, and tan(θ) = opposite/adjacent. For a unit circle approach, sin(θ) is the y-coordinate and cos(θ) is the x-coordinate of the point on the circle at angle θ. Tangent equals sin(θ)/cos(θ) and has asymptotes where cos(θ) = 0 (at 90 deg and 270 deg). The calculator handles all real angle inputs and properly identifies undefined cases. Trigonometric functions have a period of 360 deg for sine and cosine, and 180 deg for tangent.
Regional Notes
India (IN): Trigonometry is a core part of the CBSE, ICSE, and state board mathematics curriculum from Class 10 onward. Students commonly use trigonometric tables and now online calculators for verifying sin, cos, and tan values of standard angles (0 deg, 30 deg, 45 deg, 60 deg, 90 deg) during board exam preparation.
United States (US): Trigonometry is taught in high school pre-calculus and college-level math courses aligned with Common Core standards. The sine, cosine, and tangent functions are widely used in engineering disciplines, physics labs, and computer graphics at universities nationwide.
United Kingdom (UK): Trigonometric functions are a key component of GCSE and A-Level Mathematics syllabi. Students preparing for exams from AQA, Edexcel, OCR, and WJEC exam boards regularly practice trig ratio problems with right triangles and the unit circle.
Frequently Asked Questions
What is sine, cosine, and tangent?
Sine (sin), cosine (cos), and tangent (tan) are the three primary trigonometric functions that relate the angles of a right triangle to the ratios of its sides. For an angle θ in a right triangle, sin(θ) = opposite/hypotenuse, cos(θ) = adjacent/hypotenuse, and tan(θ) = opposite/adjacent. They are fundamental to trigonometry, geometry, physics, and engineering.
How do you calculate sine, cosine, and tangent on a calculator?
To calculate sin, cos, or tan of an angle on this calculator, simply enter the angle in degrees and click Calculate. The calculator instantly shows sin(θ), cos(θ), and tan(θ) values. For special angles like 0 deg, 30 deg, 45 deg, 60 deg, and 90 deg, trigonometric functions have well-known exact values that you can check against the calculator output.
What are the key values of sin, cos, and tan for common angles?
Common angles and their trig values: 0 deg -> sin=0, cos=1, tan=0; 30 deg -> sin=0.5, cos=sqrt3/2≈0.8660, tan=1/sqrt3≈0.5774; 45 deg -> sin=cos=sqrt2/2≈0.7071, tan=1; 60 deg -> sin=sqrt3/2≈0.8660, cos=0.5, tan=sqrt3≈1.732; 90 deg -> sin=1, cos=0, tan=undefined. The interactive graph shows how these functions behave across 0 deg to 360 deg.
When does tan become undefined?
Tangent is undefined when cos(θ) = 0, which occurs at 90 deg and 270 deg (and every 180 deg interval thereafter). At these angles, the tangent function has vertical asymptotes because dividing by zero yields an undefined result. Our calculator displays 'undefined' for such cases.
What is the range of sine, cosine, and tangent functions?
Sine and cosine values always range between -1 and 1 inclusive for all real angle inputs. The tangent function has no bounds -- its range is all real numbers (-∞ to ∞) because it is the ratio of sine to cosine and can grow arbitrarily large as cos(θ) approaches zero.
How are trigonometric functions used in real life?
Trigonometric functions are used extensively in physics (wave motion, oscillations, projectile motion), engineering (structural analysis, signal processing, electrical circuits), architecture (roof pitch calculations, bridge design), astronomy (calculating distances to stars), computer graphics (rotation matrices, 3D rendering), and navigation (GPS, maritime routes). Understanding sin, cos, and tan is essential for STEM fields worldwide.
What is the relationship between sin and cos?
Sine and cosine are phase-shifted by 90 deg: sin(θ) = cos(90 deg - θ) and cos(θ) = sin(90 deg - θ). They follow the Pythagorean identity sin^2(θ) + cos^2(θ) = 1 for any angle θ. The graph shows that when sine reaches its maximum (1), cosine is at zero, and vice versa.
How do you convert degrees to radians for trig functions?
To convert degrees to radians, multiply the angle in degrees by pi/180. For example, 30 deg = 30 x pi/180 = pi/6 radians ≈ 0.5236 radians. Our calculator handles the conversion internally -- just enter the angle in degrees.