About this calculator
The Sine Calculator finds sin(x) for an angle in degrees or radians and shows cosine and tangent alongside it for context. It is helpful for right-triangle problems, unit circle revision, waves, circular motion, and checking calculator-mode mistakes.
sine calculator method
In a right triangle, sine is the opposite side divided by the hypotenuse. Numerically, the calculator converts degrees to radians if needed and applies the sine function.
- sin(theta) = opposite / hypotenuse
- radians = degrees x pi / 180
- sin(theta) is the y-coordinate on the unit circle
How to use the sine calculator
- Enter the angle.
- Choose degrees or radians.
- Read the sine result.
- Check cosine and tangent for context.
- Compare with common angle values if the angle is familiar.
- Use enough decimal places for your working.
Worked examples
Common angle
Input: 30 degrees
Calculation: sin(30 degrees)
Result: 0.5
Right triangle ratio
Input: Opposite 7, hypotenuse 14
Calculation: sin(theta) = 7 / 14
Result: 0.5, so theta is 30 degrees for the principal acute angle
Where sine appears
Sine is used in right-triangle side calculations, waves, oscillation, bearings, vectors, and circular motion. In school maths it often appears first through SOHCAHTOA.
Sine range
Sine values are always between -1 and 1. Positive and negative signs depend on the quadrant of the angle.
Common mistakes to avoid
- Mixing degrees and radians
- Most wrong trigonometry answers come from using the wrong angle unit. Check whether the question, calculator, or exam setting is using degrees or radians before comparing results.
- Rounding too early
- Keep extra decimal places during working, then round the final answer. Rounding sine, cosine, or tangent too early can noticeably change a side length or angle.
- Using trig on a non-right triangle
- SOHCAHTOA only applies directly to right-angled triangles. Other triangles may need the sine rule, cosine rule, or a split into right triangles.
Edge cases
- Tangent is undefined where cosine is zero, such as 90 degrees and 270 degrees.
- Inverse sine and inverse cosine only accept inputs from -1 to 1.
- Angles that differ by 360 degrees can have the same sine, cosine, and tangent values.
- A calculated triangle side should not be negative. Recheck the selected side labels if that happens.
Limitations
This calculator is for educational maths support. It uses standard trigonometric formulas and JavaScript Math functions, so results are numerical approximations. For coursework, exams, engineering, surveying, or safety-critical work, follow the required method, units, precision, and marking guidance.
Frequently asked questions
Should I use degrees or radians?
Use the unit given in the question. GCSE-style triangle questions usually use degrees. A-Level maths, calculus, circular motion, and many scientific formulas often use radians.
What does SOHCAHTOA mean?
SOHCAHTOA is a memory aid: sine equals opposite over hypotenuse, cosine equals adjacent over hypotenuse, and tangent equals opposite over adjacent.
Why is tan 90 degrees undefined?
Tangent is sine divided by cosine. At 90 degrees, cosine is zero, so the division is not defined.
Why do inverse trig calculators sometimes give only one angle?
Inverse trig functions return a principal value. Some trig equations have multiple valid angles over a larger interval, so the calculator result may be one of several possible angles.
Can I use these calculators for GCSE and A-Level revision?
Yes, they are useful for checking working and building confidence. Always practise writing the full method because exam marks often depend on the steps, not just the final number.
Related calculators
- Trigonometry Calculator
- SOHCAHTOA Calculator
- Cosine Calculator