Answer first
What this calculator tells you
Calculate the sine, cosine and tangent of an angle in degrees. Read the three basic ratios for an angle you need on a slope, a ramp or a triangle. Formula: Sine, cosine and tangent of the angle (sin θ, cos θ, tan θ), with degrees converted to radians by × π ÷ 180. At the worked-example inputs, the sine is 0.5. Holding every other input steady, moving angle (degrees) from 24 to 36 moves the result from 0.407 to 0.588.
Transparent method
The formula
Read the three basic ratios for an angle you need on a slope, a ramp or a triangle.
Worked example
Example inputs
How to interpret the result
Sine, cosine and tangent are the three ratios of a right triangle's sides, and they depend only on the angle. At 30 degrees the sine is exactly one half, the cosine is about 0.866 and the tangent is about 0.577. The tangent doubles as a slope: a 30 degree ramp rises 0.577 for every unit it runs, which is how builders turn an angle into a rise.
At the worked-example inputs the sine is 0.5. It rises with angle (degrees).
Formulas assume ideal geometric shapes. Real-world measurements carry their own error, and every input must use the same unit: mixing feet and inches silently produces a wrong answer.
Before you rely on it
What to check
Check the angle unit. A calculator set to radians reads 30 as a very different angle and returns values that look plausible but are wrong.
The common error
Where people go wrong with trigonometry calculator
Expecting a tangent at 90 degrees. The ratio has no value there, because the run is zero, so the page shows a dash instead of a huge number.
Sensitivity evidence
How angle (degrees) changes the sine
Holding every other input at the worked-example value, moving angle (degrees) from 24 to 36 moves the sine from 0.407 to 0.588: a spread of 0.181, or 36% of the worked-example result.
| Angle (degrees) | Sine | Cosine | Tangent |
|---|---|---|---|
| 24 | 0.407 | 0.914 | 0.445 |
| 27 | 0.454 | 0.891 | 0.51 |
| 30worked example | 0.5 | 0.866 | 0.577 |
| 33 | 0.545 | 0.839 | 0.649 |
| 36 | 0.588 | 0.809 | 0.727 |
Step by step
The worked example, input by input
| Input | Value used | What it means |
|---|---|---|
| Angle (degrees) | 30 | Enter the angle (degrees) used in this calculation. |
| Sine | 0.5 | |
| Cosine | 0.866 | |
| Tangent | 0.577 | |
Inputs, definitions and assumptions
Angle (degrees)
Enter the angle (degrees) used in this calculation. The prefilled worked-example value is 30.
How to use this calculator
- 1Verify the inputs. Gather angle (degrees) from your own documents; the prefilled values are examples.
- 2Save a baseline. The worked example puts the sine at 0.5. Store your own version of it as Scenario A.
- 3Test one change. Start with angle (degrees), the input with the biggest effect here: moving angle (degrees) from 27 to 33 takes the sine from 0.454 to 0.545, a swing of 18% of the worked-example figure.
- 4Check the extremes. At half the example angle (degrees) (15) the sine is 0.259; at double (60) it is 0.866.
People also ask
Frequently asked questions
How do you calculate trigonometry?
Sine, cosine and tangent of the angle (sin θ, cos θ, tan θ), with degrees converted to radians by × π ÷ 180. At the worked-example inputs the sine is 0.5.
What does the trigonometry result mean?
Read the three basic ratios for an angle you need on a slope, a ramp or a triangle. At the worked-example inputs the sine is 0.5. It rises with angle (degrees).
How much does angle (degrees) change the sine?
Holding every other input at the worked-example value, moving angle (degrees) from 24 to 36 moves the sine from 0.407 to 0.588, a spread of 0.181.
What are the limits of this trigonometry calculator?
Formulas assume ideal geometric shapes. Real-world measurements carry their own error, and every input must use the same unit: mixing feet and inches silently produces a wrong answer. The tables on this page test angle (degrees) only from 24 to 36; a value outside that range is not tabulated here.
If I double angle (degrees) in the trigonometry calculator, does the sine double?
Doubling it from 30 to 60 takes the sine from 0.5 to 0.866, which is 1.73 times the worked-example figure. So it grows, but by less than double. Halving it to 15 gives 0.259.
Which inputs change the cosine in the trigonometry calculator?
At the worked-example inputs it is 0.866. Angle (degrees) takes it from 0.891 to 0.839.
Which inputs change the tangent in the trigonometry calculator?
At the worked-example inputs it is 0.577. Angle (degrees) takes it from 0.51 to 0.649.
Why is a cone's volume exactly a third of a cylinder's?
For the same base radius and height, a cone tapers linearly to a point while a cylinder maintains its full cross-section throughout: integrating that taper over the height works out to exactly one-third the cylinder's volume, a result provable with calculus but true regardless of the specific dimensions.
How do I find the area of an irregular shape?
Split it into rectangles, triangles, trapezoids and circles, work out each one, and add the areas. Subtract any cut-outs. The more pieces you use, the closer the total gets to the true area.
Sources and evidence
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