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I need to find the irrational form of Sin[7*\[Pi]/8]. But in Mathematica, I can get its numerical value. I am getting

Sin[\[Pi]/4]=1/Sqrt[2] 

in Mathematica. What I meant is an answer something like this for Sin[7*\[Pi]/8] as well. Is that possible?

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    $\begingroup$ it is hard to understand what you are asking. But if you mean you want Mathematica not to automatically write Sin[Pi/4] as 1/Sqrt[2], you can check this answer prevent-simplification-of-trig-functions $\endgroup$
    – Nasser
    Commented Jun 21, 2021 at 2:30

1 Answer 1

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The following does the job.

Sin[7*\[Pi]/8] // ToRadicals

Sqrt[2 - Sqrt[2]]/2

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