This online calculator allows you to quickly compute the values of trigonometric functions — sine (sin), cosine (cos), tangent (tan), and cotangent (cot) — for any angle specified in degrees or radians. Enter the angle value in the form below, select the unit of measurement, and get an instant result precise to several decimal places.
The calculator is useful for school and college students solving geometry and algebra problems, as well as engineers and designers who need quick trigonometric calculations without manual table lookups.
Calculator
How to Use the Calculator
- Enter the angle value in the input field.
- Select the unit of measurement — degrees or radians.
- Click the "Calculate" button.
- The calculator will immediately display the values of sin, cos, tan, cot, as well as sec and csc — depending on the selected function.
If you need to perform the inverse operation — find the angle by a known function value — please use our inverse trigonometric calculator.
Formulas of Trigonometric Functions
Trigonometric functions describe the ratio of sides in a right triangle relative to one of the acute angles:
- sin(α) = opposite side / hypotenuse
- cos(α) = adjacent side / hypotenuse
- tan(α) = sin(α) / cos(α) = opposite side / adjacent side
- cot(α) = cos(α) / sin(α) = adjacent side / opposite side
Relationship Between Degrees and Radians
An angle can be measured in degrees or radians. The conversion formula is:
α (rad) = α (deg) × π / 180
For example, 180° corresponds to π radians, and 90° corresponds to π/2 radians.
Table of Trigonometric Function Values for Major Angles
| Angle (degrees) | Angle (radians) | sin | cos | tan | cot |
|---|---|---|---|---|---|
| 0° | 0 | 0 | 1 | 0 | does not exist |
| 30° | π/6 | 1/2 | √3/2 | √3/3 | √3 |
| 45° | π/4 | √2/2 | √2/2 | 1 | 1 |
| 60° | π/3 | √3/2 | 1/2 | √3 | √3/3 |
| 90° | π/2 | 1 | 0 | does not exist | 0 |
| 120° | 2π/3 | √3/2 | -1/2 | -√3 | -√3/3 |
| 180° | π | 0 | -1 | 0 | does not exist |
| 270° | 3π/2 | -1 | 0 | does not exist | 0 |
| 360° | 2π | 0 | 1 | 0 | does not exist |
This table covers the most commonly used angles that frequently appear in school and engineering tasks.
Calculation Examples
Example 1. Calculating sin and cos for a 30° angle
Given angle α = 30°.
- sin(30°) = 0.5
- cos(30°) = 0.866
- tan(30°) = 0.577
- cot(30°) = 1.732
Example 2. Calculating tangent of an angle in radians
Given angle α = π/4 (0.785 rad), which corresponds to 45°.
- tan(π/4) = 1
Example 3. Angle greater than 90°
Given angle α = 150°.
- sin(150°) = 0.5
- cos(150°) = -0.866
Note: for angles in the second quadrant (90°–180°), the cosine takes a negative value, while the sine remains positive.
Frequently Asked Questions
How do I convert degrees to radians?
Multiply the angle value in degrees by π and divide by 180. For example, 60° × π / 180 = π/3 radians ≈ 1.047 rad.
Why does the tangent of a 90° angle not exist?
Tangent is calculated as sin(α)/cos(α). At α = 90°, the cosine is zero, and division by zero is impossible, so tan(90°) is undefined.
What is the difference between tangent and cotangent?
Cotangent is the reciprocal of tangent: cot(α) = 1/tan(α) = cos(α)/sin(α). Where tangent does not exist (e.g., 90°), cotangent is zero, and vice versa.
Can sine or cosine be greater than 1?
No. The values of sine and cosine are always in the range from -1 to 1, because they are defined as the ratio of a leg to the hypotenuse, and the hypotenuse is always the longest side of a right triangle.
How do I find the angle from a known sine or cosine value?
For this, inverse trigonometric functions are used — arcsine, arccosine, arctangent, and arccotangent. You can calculate the angle from its function value on our site.