What this calculator does
This trigonometric function calculator evaluates all six standard trig functions — sine, cosine, tangent, cosecant, secant and cotangent — for any angle you enter. You can supply the angle in degrees or radians, and the tool converts internally before computing each value.
How to use it
Enter your angle, choose whether it is in degrees or radians, and submit. The headline result shows \(\sin\theta\), and the table below lists cos, tan, and the three reciprocal functions csc, sec and cot. Values are shown to six decimal places. Where a function is undefined (for example tan at 90° or csc at 0°), the value is reported as 0 to avoid an infinite result.
The formulas explained
The three primary functions come directly from the unit circle: \(\sin\theta\) is the vertical coordinate, \(\cos\theta\) the horizontal coordinate, and \(\tan\theta = \sin\theta/\cos\theta\) is their ratio. The reciprocal functions are simply inverses:
$$\csc\theta = \frac{1}{\sin\theta},\quad \sec\theta = \frac{1}{\cos\theta},\quad \cot\theta = \frac{1}{\tan\theta} = \frac{\cos\theta}{\sin\theta}$$
Worked example
For \(\theta = 30°\), convert to radians (\(\pi/6 \approx 0.523599\)). Then
$$\sin(30°) = 0.5,\quad \cos(30°) \approx 0.866025,\quad \tan(30°) \approx 0.577350$$The reciprocals are
$$\csc(30°) = 2,\quad \sec(30°) \approx 1.154701,\quad \cot(30°) \approx 1.732051$$FAQ
Degrees or radians? Calculators and geometry usually use degrees; calculus and physics typically use radians. Pick the matching unit so your result is correct.
Why is tan undefined at 90°? Because \(\cos(90°) = 0\) and dividing by zero is undefined; the tangent grows without bound there.
What range of angles can I enter? Any real number — angles beyond 360° or negative angles are handled correctly thanks to the periodic nature of trig functions.
