Trigonometry Calculator
A 30-degree angle in a right triangle gives sin = 0.5, cos = 0.866, and tan = 0.577. This trigonometry calculator computes all six trig ratios and all three side lengths from an angle and one known side using right-triangle trig.
Quick answer
sin is opposite over hypotenuse, cos is adjacent over hypotenuse, tan is opposite over adjacent.
What this tells you
- •sin is opposite over hypotenuse, cos is adjacent over hypotenuse, tan is opposite over adjacent.
- •csc, sec, and cot are the reciprocals of sin, cos, and tan.
- •Pick which side you know (opposite, adjacent, or hypotenuse) and the calculator solves for the other two.
How to Use
- 1Enter an acute angle between 0 and 90 degrees.
- 2Choose which side length you know: opposite, adjacent, or hypotenuse.
- 3Click Calculate to get all six trig ratios and the three side lengths.
How It Works
Formula
sin = opp/hyp, cos = adj/hyp, tan = opp/adj. csc = 1/sin, sec = 1/cos, cot = 1/tan.The calculator uses right-triangle trigonometry. Given an angle A and one side length, it normalizes the known side to 1 and solves for the other two sides using the sine, cosine, and tangent definitions. The reciprocal functions follow directly.
Calculation note: values are processed in the order shown above, using the current input units.
Worked Examples
30 degrees, opposite = 1
With the opposite side set to 1, the hypotenuse is 1 / sin(30) = 2, and the adjacent side is 1 / tan(30) = 1.732. This matches the 30-60-90 triangle proportions.
45 degrees, hypotenuse = 1
In a 45-45-90 triangle, both legs are equal and the hypotenuse is the square root of 2 times a leg. With the hypotenuse at 1, each leg is 1 / sqrt(2) = 0.7071.
Common Trig Values
Sine, cosine, and tangent for the most common angles.
| Angle | sin | cos | tan |
|---|---|---|---|
| 30 deg | 0.5 | 0.866 | 0.577 |
| 45 deg | 0.707 | 0.707 | 1 |
| 60 deg | 0.866 | 0.5 | 1.732 |
| 36.87 deg | 0.6 | 0.8 | 0.75 |
| 53.13 deg | 0.8 | 0.6 | 1.333 |
Common mistakes
- Entering the angle in radians instead of degrees. This calculator expects degrees. Convert radians to degrees by multiplying by 180 and dividing by pi.
- Using the wrong side for the ratio. sin uses opposite over hypotenuse, not adjacent over hypotenuse.
- Confusing sin(30) with sin(0.5). sin(30 degrees) is 0.5, not the sine of 0.5 radians.