# When you do inverse trig, when you find the answer would you have to round the angle or can you keep it as a decimal until stated to round?

### 4 Answers

- PopeLv 73 weeks ago
If it is irrational, as is often the case, then whatever decimal form you have is rounded anyway. It would only be a matter of deciding how many decimal places to leave. No one evaluating your work is likely going to want to see 12 significant figures, even if they are correct. Take this example, the dihedral angle of a regular icosahedron:

Exact answer: cos⁻¹[-√(5)/3]

You really cannot beat an exact answer, but it may not be so useful if it is being applied in some way.

In degrees to 12 significant figures: 138.189685104°

This may be useful in an application, but not as a quiz answer.

I am now recalling an answer I once saw, where the student gave the distance between a rescue helicopter and a stranded hiker the the nearest 10⁻¹⁰ meters. Think about that.

Nearest 0.1°: 138.2°

Less precise, but this is more practical.

In any case, you should be asking whoever it is who evaluates the answers.

On a related note, learn to use the storage registers in your calculator. If you are writing down 12-digit intermediate values, then you are wasting time, and just asking for a slip-up. If you are writing down only three significant figures, and then putting those values back into the calculation, then you are compromising the precision.

- Anonymous3 weeks ago
It is best to use unrounded values and only round when required (usually when giving a final answer).

This is fine when using a calculator but is impractical if you have to write-down intermediate results. In this case, the usual practice it to work to 2 more significant figures than required in the final answer.

This is not just when using inverse trig functions – it is general advice.