Trig Function
Compute sine, cosine, tangent, cosecant, secant, and cotangent for any angle in degrees or radians. Free online trigonometry calculator with instant results for all six trigonometric functions.
About This Calculator
The Trig Function Calculator is a comprehensive tool for computing all six trigonometric functions -- sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), and cotangent (cot) -- for any angle in degrees or radians. This calculator is designed for students studying trigonometry at high school or college level, teachers preparing lesson materials, engineers working with angles and periodic functions, and anyone who needs quick and accurate trigonometric values.
The calculator uses JavaScript's built-in Math functions for precise computation. For degree mode, the angle is first converted to radians using the formula theta_rad = theta_deg x pi/180, then each trig function is computed. For radian mode, the angle is used directly. The six functions are defined as: sin(theta) = opposite/hypotenuse, cos(theta) = adjacent/hypotenuse, tan(theta) = sin(theta)/cos(theta), csc(theta) = 1/sin(theta), sec(theta) = 1/cos(theta), cot(theta) = cos(theta)/sin(theta). When a function involves division by zero (e.g., tan(90 deg) or csc(0 deg)), the calculator displays undefined.
The calculator supports both degrees (the most common unit in everyday geometry and navigation) and radians (the standard unit in calculus, physics, and advanced mathematics). Results are displayed to six decimal places for precision, and the calculator also shows the input angle in radians for cross-reference.
Regional Notes
India (IN): Trigonometry is taught extensively in CBSE and state board curricula from Class 10 onward. Students preparing for JEE and other engineering entrance exams regularly use these functions for calculus, physics, and geometry problems.
United States (US): Trigonometry is a core part of the high school mathematics curriculum, typically covered in Algebra 2 and Precalculus courses. The functions are used extensively in college-level STEM programs including engineering, physics, and computer science.
United Kingdom (UK): Trigonometry is introduced at GCSE level and studied in depth at A-Level Mathematics and Further Mathematics. Students use these functions in mechanics, pure mathematics, and physics applications.
Frequently Asked Questions
What are the six trigonometric functions?
The six trigonometric functions are sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), and cotangent (cot). Sine is opposite over hypotenuse, cosine is adjacent over hypotenuse, and tangent is opposite over adjacent. Cosecant, secant, and cotangent are their respective reciprocals.
How do you convert degrees to radians?
To convert degrees to radians, multiply the degree value by pi/180. For example, 45 deg x pi/180 = pi/4 ≈ 0.7854 radians. This calculator does the conversion automatically when you select degree mode.
What is the difference between degrees and radians?
Degrees and radians are two units for measuring angles. A full circle is 360 deg or 2pi radians. Degrees are commonly used in everyday geometry and navigation, while radians are the standard unit in calculus, physics, and advanced mathematics because they simplify many formulas.
When is tan(theta) undefined?
Tangent is undefined when cos(theta) = 0, which occurs at odd multiples of 90 deg (pi/2 radians), such as 90 deg, 270 deg, 450 deg, etc. At these angles, the tangent function approaches positive or negative infinity because the adjacent side length becomes zero in the unit circle definition.
How are trig functions used in real life?
Trigonometric functions are used in architecture to calculate roof slopes and bridge loads, in engineering for signal processing and AC circuit analysis, in navigation for GPS and celestial navigation, in physics to describe wave motion and periodic phenomena, and in computer graphics to create rotations and animations.
What are the values of trig functions for common angles?
For 0 deg: sin=0, cos=1, tan=0. For 30 deg: sin=0.5, cos=sqrt3/2≈0.866, tan=1/sqrt3≈0.577. For 45 deg: sin=cos=sqrt2/2≈0.707, tan=1. For 60 deg: sin=sqrt3/2≈0.866, cos=0.5, tan=sqrt3≈1.732. For 90 deg: sin=1, cos=0, tan undefined. These exact values are fundamental in trigonometry.
How do you find the reciprocal trig functions?
Cosecant (csc) is the reciprocal of sine: csc(theta) = 1/sin(theta). Secant (sec) is the reciprocal of cosine: sec(theta) = 1/cos(theta). Cotangent (cot) is the reciprocal of tangent: cot(theta) = 1/tan(theta) = cos(theta)/sin(theta). When sin(theta) or cos(theta) is zero, the corresponding reciprocal is undefined.
Why does the calculator show undefined for some trig functions?
Some trig functions are undefined at specific angles because they involve division by zero. For example, tan(90 deg) = sin/cos = 1/0, which is undefined (infinity). The calculator displays undefined in these cases, which is mathematically correct.