diff --git a/tests/unit_circle_test.cc b/tests/unit_circle_test.cc
index fc2d9a1..f5c0d96 100644
--- a/tests/unit_circle_test.cc
+++ b/tests/unit_circle_test.cc
@@ -15,7 +15,7 @@ template <typename TYPE, typename PRECISE>
 void test(int MAX)
 {
 	for (int N = 1; N <= MAX; ++N) {
-		for (int n = 0; n < N; ++n) {
+		for (int n = -N; n <= N; ++n) {
 			PRECISE x = DSP::Const<PRECISE>::TwoPi() * PRECISE(n) / PRECISE(N);
 			PRECISE cos_err = std::abs(DSP::UnitCircle<TYPE>::cos(n, N) - std::cos(x));
 			assert(cos_err < std::numeric_limits<TYPE>::epsilon());
diff --git a/unit_circle.hh b/unit_circle.hh
index 0df6b85..67e6cbd 100644
--- a/unit_circle.hh
+++ b/unit_circle.hh
@@ -56,6 +56,10 @@ public:
 	static constexpr TYPE cos(int n, int N)
 	{
 		return
+			8*n <-7*N ? cosine_approx(rad(n+N, N)) :
+			8*n <-5*N ? -sine_approx(rad(4*n+3*N, 4*N)) :
+			8*n <-3*N ? -cosine_approx(rad(2*n+N, 2*N)) :
+			8*n <-1*N ? sine_approx(rad(4*n+N, 4*N)) :
 			8*n < 1*N ? cosine_approx(rad(n, N)) :
 			8*n < 3*N ? -sine_approx(rad(4*n-N, 4*N)) :
 			8*n < 5*N ? -cosine_approx(rad(2*n-N, 2*N)) :
@@ -65,6 +69,10 @@ public:
 	static constexpr TYPE sin(int n, int N)
 	{
 		return
+			8*n <-7*N ? sine_approx(rad(n+N, N)) :
+			8*n <-5*N ? cosine_approx(rad(4*n+3*N, 4*N)) :
+			8*n <-3*N ? -sine_approx(rad(2*n+N, 2*N)) :
+			8*n <-1*N ? -cosine_approx(rad(4*n+N, 4*N)) :
 			8*n < 1*N ? sine_approx(rad(n, N)) :
 			8*n < 3*N ? cosine_approx(rad(4*n-N, 4*N)) :
 			8*n < 5*N ? -sine_approx(rad(2*n-N, 2*N)) :