#include<bits/stdc++.h>
using namespace std;
#define int long long
#define db double
const int N = 200010;
struct node {
	int u, l, r; db si, co; int lzy;
} tr[N * 4];
int a[N];
void pushup(int u) {
	tr[u].si = tr[u << 1].si + tr[u << 1 | 1].si;
	tr[u].co = tr[u << 1].co + tr[u << 1 | 1].co;
}
void upd(int u, int x) {
	db si = tr[u].si, co = tr[u].co;
	tr[u].si = si * cos(x) + co * sin(x);
	tr[u].co = co * cos(x) - si * sin(x);
	tr[u].lzy += x;
}
void pushdown(int u) {
	if(!tr[u].lzy) return ;
	upd(u << 1, tr[u].lzy);
	upd(u << 1 | 1, tr[u].lzy);
	tr[u].lzy = 0;
}
void build(int u, int l, int r) {
	tr[u].l = l, tr[u].r = r;
	if(l == r) {
		tr[u].si = sin(a[l]);
		tr[u].co = cos(a[l]);
		return ;
	}
	int mid = l + r >> 1;
	build(u << 1, l, mid);
	build(u << 1 | 1, mid + 1, r);
	pushup(u);
}
void upd(int u, int l, int r, int k) {
	if(l <= tr[u].l && tr[u].r <= r) {
		upd(u, k);
		tr[u].lzy += k;
		return ;
	}
	pushdown(u);
	int mid = tr[u].l + tr[u].r >> 1;
	if(l <= mid) upd(u << 1, l, r, k);
	if(mid < r)  upd(u << 1 | 1, l, r, k);
	pushup(u);
}
db ask(int u, int l, int r) {
	if(l <= tr[u].l && tr[u].r <= r) return tr[u].si;
	db ans = 0;
	pushdown(u);
	int mid = tr[u].l + tr[u].r >> 1;
	if(l <= mid) ans += ask(u << 1, l, r);
	if(mid < r)  ans += ask(u << 1 | 1, l, r);
	return ans;
}
signed main() {
	int n; scanf("%lld", &n);
	for(int i = 1; i <= n; i++) scanf("%lld", &a[i]);
	build(1, 1, n);
	int q; scanf("%lld", &q);
	while(q--) {
		int o, l, r; scanf("%lld%lld%lld", &o, &l, &r);
		if(o == 1) {
			int k; scanf("%lld", &k);
			upd(1, l, r, k);
		}
		if(o == 2) {
			printf("%.1lf\n", ask(1, l, r));
		}
	}
	return 0;
}