About this calculator
The Inverse Trig Calculator finds angles from sine, cosine, and tangent values using arcsin, arccos, and arctan. It is useful when a ratio is known and the missing angle is needed, especially in SOHCAHTOA and coordinate geometry work.
inverse trig calculator method
Inverse trig functions undo the basic trig ratios over their principal ranges. Arcsin and arccos require inputs from -1 to 1, while arctan accepts any real number.
- theta = arcsin(value), where -1 <= value <= 1
- theta = arccos(value), where -1 <= value <= 1
- theta = arctan(value)
- degrees = radians x 180 / pi
How to use the inverse trig calculator
- Choose arcsin, arccos, or arctan.
- Enter the known trig ratio.
- Choose degrees or radians for the answer.
- Check any domain warning shown by the calculator.
- Read the principal angle.
- Consider whether the original problem has another valid angle in a wider interval.
Worked examples
Arcsin of 0.5
Input: arcsin(0.5)
Calculation: theta = sin^-1(0.5)
Result: 30 degrees
Arctan of 1
Input: arctan(1)
Calculation: theta = tan^-1(1)
Result: 45 degrees
Principal values
Inverse trig calculators usually return a principal value. For example, sin(theta) = 0.5 has more than one solution over 0 to 360 degrees, but arcsin(0.5) returns 30 degrees as the principal value.
Domain checks
A sine or cosine ratio cannot be greater than 1 or less than -1. If a triangle calculation produces such a value, the measurements are inconsistent or have been entered against the wrong side labels.
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
- Radians to Degrees Calculator