#include<iostream>
#include<cmath>
using namespace std;
int n, m;
long long a[200010];
long long tag[800010];
struct node {
    double sin, cos;
}tr[800010];
void pushup(int u, double sinx, double cosx) {
    double sinu = tr[u].sin, cosu = tr[u].cos;
    tr[u].sin = sinu * cosx + cosu * sinx;
    tr[u].cos = cosu * cosx - sinu * cosx;
}
void pushdown(int u) {
    if(!tag[u]) return;
    tag[u << 1] += tag[u];
    tag[u << 1 | 1] += tag[u];
    double sinu = sin(tag[u]), cosu = cos(tag[u]);
    pushup(u << 1,sinu, cosu);
    pushup(u << 1 | 1,sinu, cosu);
    tag[u] = 0;
}
void build(int u, int l, int r) {
    if(l == r) {
        tr[u] = {sin(a[l]), cos(a[l])};
        return;
    }
    int mid = l + r >> 1;
    build(u << 1, l, mid);
    build(u << 1 | 1, mid + 1, r);
    tr[u].sin = tr[u << 1].sin + tr[u << 1 | 1].sin;
    tr[u].cos = tr[u << 1].cos + tr[u << 1 | 1].cos;
}
void update(int u, int l, int r, int x, int y, int k, double sink, double cosk) {
    if(x <= l && r <= y) {
        pushup(u, sink, cosk);
        tag[u] += k;
        return;
    }
    int mid = l + r >> 1;
    pushdown(u);
    if(x <= mid) update(u << 1, l, mid, x, y, k, sink, cosk);
    if(y > mid) update(u << 1 | 1, mid + 1, r, x, y, k, sink, cosk);
    tr[u].sin = tr[u << 1].sin + tr[u << 1 | 1].sin;
    tr[u].cos = tr[u << 1].cos + tr[u << 1 | 1].cos;
}
double query(int u, int l, int r, int x, int y) {
    if(x <= l && r <= y) return tr[u].sin;
    pushdown(u);
    int mid = l + r >> 1;
    double ans = 0.0;
    if(x <= mid) ans += query(u << 1, l, mid, x, y);
    if(y > mid) ans += query(u << 1 | 1, mid + 1, r, x, y);
    return ans;
}
int main() {
    ios::sync_with_stdio(false);
    cin.tie(0); cout.tie(0);
    cin >> n;
    for(int i = 1; i <= n; i ++) cin >> a[i];
    build(1, 1, n);
    cin >> m;
    for(int i = 1; i <= m; i ++) {
        int op, l, r, w;
        cin >> op >> l >> r;
        if(op == 1) {
            cin >> w;
            update(1, 1, n, l, r, w, sin(w), cos(w));
        }
        else printf("%.1lf\n", query(1, 1, n, l, r));
    }
    return 0;
}