# Confused by SolveValues Output [closed]

When I plug in an equation involving ArcSin to SolveValues, I get a result involving Root and a pure function, with the answer embeded.

Here is a simplified version of the equation:

SolveValues[1 == a ArcSin[a], a, Assumptions -> 0 <= a <= 1 ]


Output:

{
Root[{
-1 + ArcSin[#] # &,
0.8975394612804871843930734619620943415620.300813366021398
}]
}


The long string of digits is the answer I want, but why is it given inside this expression, and how to I get it out?

• Try this: FindRoot[1 == a ArcSin[a], {a, 0.5}]. Oct 1, 2022 at 15:12
• The Root expression is the exact solution, i.e., an exact number. Like any other exact number (e.g., Sin[2]), use N to convert it to an approximate value. Oct 1, 2022 at 15:14
• I know the first part, I was including it in an answer to my own post! The second part is what I didn't know Oct 1, 2022 at 15:15
• Oct 1, 2022 at 15:17
• Thanks for that reference, @MichaelE2. Oct 1, 2022 at 15:20

Try this:

NSolveValues[1 == a ArcSin[a] && 0 <= a <= 1, a]
(*{0.8975394612804872}*)


Or, as @Bob Hanlon points out:

SolveValues[1 == a ArcSin[a], a, Assumptions -> 0 <= a <= 1] // N
(*{0.8975394612804872}*)


From the documentation, the Root function "Root[{f,c}] represents the exact root of the general equation f[x] = 0 near x = c."

Since 0.8975394612804871843930734619620943415620.300813366021398 is not an exact answer,

{
Root[{
-1 + ArcSin[#] # &,
0.8975394612804871843930734619620943415620.300813366021398
}]
}
`

is given to specify the exact answer, which occurs near 0.8975...