R (+Rmpfr), 55 bytes

function(n,b=Rmpfr::mpfr(1,n)){for(i in 1:n)b=cos(b);b}

Dennis has now added Rmpfr to TIO so this will work; added some test cases.

###Explanation: Takes the code I wrote from this challenge to evaluate cos n times starting at 1, but first I specify the precision I want the values to be in by creating an object b of class mpfr with value 1 and precision n, n>=2, so we get more precision as we go along.

Try it online!

R (+Rmpfr), 55 bytes

function(n,b=Rmpfr::mpfr(1,n)){for(i in 1:n)b=cos(b);b}

Dennis has now added Rmpfr to TIO so this will work; added some test cases.

Explanation:

Takes the code I wrote from this challenge to evaluate cos n times starting at 1, but first I specify the precision I want the values to be in by creating an object b of class mpfr with value 1 and precision n, n>=2, so we get more precision as we go along.

Try it online!

R (+Rmpfr), 55 bytes

function(n,b=Rmpfr::mpfr(1,n)){for(i in 1:n)b=cos(b);b}

Dennis has now added Rmpfr to TIO so this will work; added some test cases.

Try it online!

R (+Rmpfr), 55 bytes

function(n,b=Rmpfr::mpfr(1,n)){for(i in 1:n)b=cos(b);b}

Dennis has now added Rmpfr to TIO so this will work; added some test cases.

###Explanation: Takes the code I wrote from this challenge to evaluate cos n times starting at 1, but first I specify the precision I want the values to be in by creating an object b of class mpfr with value 1 and precision n, n>=2, so we get more precision as we go along.

Try it online!

R (+Rmpfr), 55 bytes

function(n,b=Rmpfr::mpfr(1,n)){for(i in 1:n)b=cos(b);b}

Try it online!

TIO won't work because it doesn't have the Rmpfr package; trying to find a place to test it online.

R (+Rmpfr), 55 bytes

function(n,b=Rmpfr::mpfr(1,n)){for(i in 1:n)b=cos(b);b}

Dennis has now added Rmpfr to TIO so this will work; added some test cases.

Try it online!