#include <iostream>
#include <cstring>
#include <algorithm>
#include <cmath>
using namespace std;

#define N 200005
#define ls u<<1
#define rs u<<1|1
#define mid ((l+r)>>1)
int n,m,a[N];
double sinx[N<<2],cosx[N<<2];
long long tag[N<<2];
//sinx:区间正弦和, cosx:区间余弦和
//tag: 区间懒标记

void pushup(int u){ //上传
  sinx[u]=sinx[ls]+sinx[rs];
  cosx[u]=cosx[ls]+cosx[rs];
}
void pd(int u,double sinb,double cosb){
  double sina=sinx[u],cosa=cosx[u];
  sinx[u]=sina*cosb+cosa*sinb; //sin(a+b)
  cosx[u]=cosa*cosb-sina*sinb; //cos(a+b)
}
void pushdown(int u){ //下传
  if(!tag[u]) return;
  double sinb=sin(tag[u]),cosb=cos(tag[u]);
  pd(ls,sinb,cosb);
  pd(rs,sinb,cosb);
  tag[ls]+=tag[u];
  tag[rs]+=tag[u];
  tag[u]=0; //清空懒标记
}
void build(int u,int l,int r){ //建树
  if(l==r){
    sinx[u]=sin(a[l]);
    cosx[u]=cos(a[l]);
    return;
  }
  build(ls,l,mid);
  build(rs,mid+1,r);
  pushup(u);
}
void change(int u,int l,int r,int x,int y,int k){ //区修
  if(x<=l&&r<=y){
    pd(u,sin(k),cos(k));
    tag[u]+=k;
    return;
  }
  pushdown(u);
  if(x<=mid) change(ls,l,mid,x,y,k);
  if(y>mid) change(rs,mid+1,r,x,y,k);
  pushup(u);
}
double query(int u,int l,int r,int x,int y){ //区查
  if(x<=l&&r<=y) return sinx[u];
  pushdown(u);
  double res=0;
  if(x<=mid) res=query(ls,l,mid,x,y);
  if(y>mid) res+=query(rs,mid+1,r,x,y);
  return res;
}
int main(){
  scanf("%d",&n);
  for(int i=1;i<=n;++i)scanf("%d",&a[i]);
  build(1,1,n);
  scanf("%d",&m); int op,l,r,k;
  while(m--){
    scanf("%d%d%d",&op,&l,&r);
    if(op==1){
      scanf("%d",&k);
      change(1,1,n,l,r,k);
    }
    else printf("%.3lf\n",query(1,1,n,l,r));
  }
  return 0;
}