Quick answer
For an angle θ the six trigonometric functions are sin, cos, tan, csc, sec and cot. At 30°: sin = 0.5, cos = 0.8660, tan = 0.5774, csc = 2, sec = 1.1547 and cot = 1.7321.
Enter an angle and choose degrees or radians. The calculator returns all six functions. Use this trigonometry calculator to check your own figures.
Related tools: Law of Cosines Calculator: Third side of a triangle from two sides and the included angle (law of cosines). Triangle Calculator: Area, perimeter, angles and type of a triangle from its three sides. Right Triangle Calculator: Solve a right triangle from its two legs: hypotenuse, angles, area and perimeter.
How to use the Trigonometry Calculator
- Enter angle.
- Choose unit: Degrees and Radians.
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Angle | A number | — |
| Unit | Choose one: Degrees; Radians | Starts at Degrees |
Formula and method
Formula
sin, cos, tan, csc, sec, cot of θ
IEEE-754 double precision; shown to at most 6 decimal places.
Each function is evaluated from the angle in radians; reciprocal functions report 'undefined' when their denominator is zero.
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Angle = 30; Unit = Degrees.
| Result | Value |
|---|---|
| sin | 0.5 |
| cos | 0.866025 |
| tan | 0.57735 |
| csc | 2 |
| sec | 1.154701 |
| cot | 1.732051 |
Example 2
Inputs: Angle = 90; Unit = Degrees.
| Result | Value |
|---|---|
| sin | 1 |
| cos | 0 |
| tan | undefined |
| csc | 1 |
| sec | undefined |
| cot | 0 |
The first line is the headline result (sin). Below it the trigonometry Calculator lists cos, tan, csc, sec and cot, which describe the same case from other angles. IEEE-754 double precision; shown to at most 6 decimal places.
Reciprocals
csc = 1/sin, sec = 1/cos and cot = 1/tan. At 30°: 1/0.5 = 2, 1/0.8660 = 1.1547, 1/0.5774 = 1.7321. Values that don't exist, such as tan 90°, are shown as undefined.
Useful angles
0°, 30°, 45°, 60° and 90° have exact values: sin 45° = √2/2 = 0.7071, cos 60° = 0.5. Sine and cosine lie between −1 and 1.
How the result changes with angle
Holding every other input at the first worked example, this table changes only angle. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| Angle | sin | cos | tan |
|---|---|---|---|
| 15 | 0.258819 | 0.965926 | 0.267949 |
| 30 | 0.5 | 0.866025 | 0.57735 |
| 60 | 0.866025 | 0.5 | 1.732051 |
| 120 | 0.866025 | -0.5 | -1.732051 |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Angle: entering "x" shows "Angle must be a number." beside that field and no result.
Choosing between the Trigonometry Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Law of Cosines Calculator](/math/law-of-cosines-calculator/) | side b, side c and included angle A | Side a |
| [Triangle Calculator](/math/triangle-calculator/) | side a, side b and side c | Area |
| [Right Triangle Calculator](/math/right-triangle-calculator/) | leg a and leg b | Hypotenuse c |
| [Sine Rule Calculator](/math/sine-rule-calculator/) | angle A, side a and angle B | Side b |
| [Inverse Trigonometry Calculator](/math/inverse-trigonometry-calculator/) | function and value | Angle |
Background: trigonometry
In a right triangle, sin θ is the opposite side over the hypotenuse, cos θ the adjacent side over the hypotenuse and tan θ the opposite over the adjacent. Their reciprocals are cosecant, secant and cotangent. At 30° the values are sin = 0.5, cos = 0.866025 and tan = 0.577350.
Check the angle unit before you calculate: degrees convert to radians by multiplying by π/180, so 30° is about 0.5236 rad. Some values are undefined, for example tan 90°, because the cosine is zero there and the ratio would divide by zero.
Assumptions and limitations
- Undefined values are shown as 'undefined'
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for angle to confirm this.
Frequently asked questions
What is sin 90°?
sin 90° = 1, the maximum value of sine.
Why is tan 90° undefined?
tan 90° = sin 90° ÷ cos 90° = 1 ÷ 0, so it is undefined.
How do I convert radians?
Multiply radians by 180/π: 1 rad is about 57.296°.
What does the Trigonometry Calculator calculate?
All six trigonometric functions of an angle. It returns sin, cos, tan, csc and sec.
What formula does the Trigonometry Calculator use?
sin, cos, tan, csc, sec, cot of θ. Each function is evaluated from the angle in radians; reciprocal functions report 'undefined' when their denominator is zero.
How is the result rounded or limited?
IEEE-754 double precision; shown to at most 6 decimal places. Undefined values are shown as 'undefined'.
What does the “Unit” option change?
It sets how the trigonometry is worked out. The choices are Degrees and Radians.
What is an example of a trigonometry result?
With angle 30 and unit Degrees, the sin is 0.5.
Related calculators
- Law of Cosines Calculator — Third side of a triangle from two sides and the included angle (law of cosines).
- Triangle Calculator — Area, perimeter, angles and type of a triangle from its three sides.
- Right Triangle Calculator — Solve a right triangle from its two legs: hypotenuse, angles, area and perimeter.
- Sine Rule Calculator — Apply the sine rule to find a missing side or angle of a triangle from an angle and its opposite side.
- Inverse Trigonometry Calculator — Arcsine, arccosine or arctangent in degrees and radians.
- SOHCAHTOA Calculator — Find the other two sides of a right triangle from one side and an acute angle.
- Reference Angle Calculator — Acute angle between the terminal side and the x-axis.
- Inverse Sine Calculator — arcsin (inverse trigonometric function) with the result in degrees and radians.
Sources
- Standard trigonometric definitions on the unit circle (NIST DLMF §4.14)
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.