Trigonometric Functions Calculator (Radians)

Enter Calculation

Function sin theta cos theta tan theta sin, cos, tan csc theta sec theta cot theta csc, sec, cot

Angle theta (rad) Type a number or an expression using "pi" for the constant pi (e.g. pi/6, 2pi, pi/4).

Formula

Show calculation steps (1)

1. Reciprocal functions

   

   Cosecant, secant and cotangent are the reciprocals of sine, cosine and tangent respectively.

Results

sin theta

0.5

theta = 0.5235987756 rad

Function	Value
sin theta	0.5
cos theta	0.86602540378444
tan theta	0.57735026918963

What this calculator does

This tool evaluates the six trigonometric functions of an angle theta measured in radians: sine, cosine, tangent, cosecant (csc), secant (sec) and cotangent (cot). You can pick a single function, the sin/cos/tan trio, or the reciprocal csc/sec/cot trio from the Function dropdown. It is pure mathematics and applies identically everywhere.

How to use it

Choose which functions you want from the Function selector. Then type the angle in the Angle theta field. The input is already in radians, so no degree conversion is performed. You may enter a plain decimal such as 0.5236, or a symbolic expression where the token pi stands for the constant pi: for example pi/6, 2pi, pi/4, or 3pi/2. The calculator parses the expression, substitutes pi, and reports the requested function values.

The formulas explained

Sine and cosine are the fundamental functions. Tangent is their ratio, \(\tan\theta=\frac{\sin\theta}{\cos\theta}\). The reciprocal functions are

$$\csc\theta=\frac{1}{\sin\theta},\quad \sec\theta=\frac{1}{\cos\theta},\quad \cot\theta=\frac{\cos\theta}{\sin\theta}$$

Tangent and secant are undefined wherever \(\cos\theta=0\) (at \(\theta=\pi/2+k\pi\)), and cosecant and cotangent are undefined wherever \(\sin\theta=0\) (at \(\theta=k\pi\)). In those cases the calculator reports "undefined" instead of dividing by zero. Tiny floating-point residues near exact zeros are cleaned up so results stay tidy.

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Sine and cosine are smooth waves; tangent repeats with vertical asymptotes where cosine is zero.

On the unit circle, the angle θ (in radians) gives cos θ as the x-coordinate and sin θ as the y-coordinate.

Worked example

With Function set to sin, cos, tan and Angle set to pi/6, \(\theta=0.5235987756\) rad. Then \(\sin\theta=0.5\), \(\cos\theta=0.8660254038\) (which is the square root of 3 over 2), and

$$\tan\theta=\frac{0.5}{0.8660254038}=0.5773502692$$

(which is 1 over the square root of 3). Switching to the csc, sec, cot trio for the same angle gives \(\csc=2\), \(\sec=1.1547005384\), and \(\cot=1.7320508076\) (the square root of 3).

FAQ

Are the inputs in degrees or radians? Radians. If you have degrees, multiply by \(\pi/180\) first (for example 30 degrees = \(\pi/6\)).

Why does it say "undefined"? Because the requested function divides by a quantity that is zero at that angle — for instance tan and sec at \(\pi/2\), or csc and cot at 0 or \(\pi\).

Can I type expressions? Yes. Use pi for the constant pi together with multiplication and division, such as pi/3 or 2pi/3.