Trigonometry Calculator
Find sine, cosine and tangent of an angle.
The three basic trig ratios for any angle.
How the Math Works
The Trigonometry Calculator uses the fundamental relationship between degrees and radians to compute sine, cosine, and tangent values. Since trigonometric functions in mathematics are defined using radians, the calculator first converts the input angle from degrees to radians by multiplying the degree value by π/180. Once in radians, it applies the appropriate trigonometric function: sine (opp/hyp), cosine (adj/hyp), or tangent (opp/adj) based on the unit circle definitions. This conversion ensures accurate results across all angle measurements.
Practical Applications
To use this calculator for practical problems, simply enter your angle in degrees and select whether you need sine, cosine, or tangent. For example, if you're solving a right triangle problem where you know one angle is 30 degrees and need to find the ratio of the opposite side to the hypotenuse, enter 30 and calculate sine to get 0.5. Engineers use this for calculating component forces, architects for roof angles, and programmers for game physics and rotation calculations.
Day-to-Day Use
Understanding trigonometric ratios helps in everyday situations like determining the height of a tree or building using shadow measurements, setting up proper angles for sports equipment like tennis nets or basketball hoops, or even adjusting your TV stand to achieve the optimal viewing angle. When DIY enthusiasts install ramps, shelves, or roofing materials, knowing how to calculate angles and slopes makes the difference between a safe, stable installation and one that needs costly repairs. The calculator makes these practical applications accessible without requiring memorization of complex formulas.
Worked example
30° → sin 0.5, cos 0.866, tan 0.577.
FAQ
Why does tan blow up at 90°?
cos(90°) = 0, and tan = sin ÷ cos, so it's undefined there.