diff --git a/doc/source/fmprb.rst b/doc/source/fmprb.rst
index e396b915..2d81f835 100644
--- a/doc/source/fmprb.rst
+++ b/doc/source/fmprb.rst
@@ -472,6 +472,14 @@ Elementary functions
     `|\sin(m \pm r) - \sin(m)| \le r` (this could be tightened to
     `\min(r,2)`).
 
+.. function:: void fmprb_sin_pi(fmprb_t s, const fmprb_t x, long prec)
+
+.. function:: void fmprb_cos_pi(fmprb_t c, const fmprb_t x, long prec)
+
+.. function:: void fmprb_sin_cos_pi(fmprb_t s, fmprb_t c, const fmprb_t x, long prec)
+
+    Sets `s = \sin \pi x`, `c = \cos \pi x`.
+
 .. function:: void fmprb_atan(fmprb_t z, const fmprb_t x, long prec)
 
     Sets `z = \tan^{-1} x`. Letting `d = \max(0, |m| - r)`,
diff --git a/fmprb.h b/fmprb.h
index 5330f120..afbb88e7 100644
--- a/fmprb.h
+++ b/fmprb.h
@@ -271,6 +271,10 @@ void fmprb_sin(fmprb_t s, const fmprb_t x, long prec);
 void fmprb_cos(fmprb_t c, const fmprb_t x, long prec);
 void fmprb_sin_cos(fmprb_t s, fmprb_t c, const fmprb_t x, long prec);
 
+void fmprb_sin_pi(fmprb_t s, const fmprb_t x, long prec);
+void fmprb_cos_pi(fmprb_t c, const fmprb_t x, long prec);
+void fmprb_sin_cos_pi(fmprb_t s, fmprb_t c, const fmprb_t x, long prec);
+
 void fmprb_sinh(fmprb_t z, const fmprb_t x, long prec);
 void fmprb_cosh(fmprb_t z, const fmprb_t x, long prec);
 void fmprb_sinh_cosh(fmprb_t s, fmprb_t c, const fmprb_t x, long prec);
diff --git a/fmprb/sin_cos_pi.c b/fmprb/sin_cos_pi.c
new file mode 100644
index 00000000..8703c585
--- /dev/null
+++ b/fmprb/sin_cos_pi.c
@@ -0,0 +1,155 @@
+/*=============================================================================
+
+    This file is part of ARB.
+
+    ARB is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    ARB is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License
+    along with ARB; if not, write to the Free Software
+    Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
+
+=============================================================================*/
+/******************************************************************************
+
+    Copyright (C) 2012 Fredrik Johansson
+
+******************************************************************************/
+
+#include "fmprb.h"
+
+void
+fmprb_sin_pi(fmprb_t y, const fmprb_t x, long prec)
+{
+    fmprb_t t;
+    fmprb_t u;
+    fmpz_t v;
+
+    fmprb_init(t);
+    fmprb_init(u);
+    fmpz_init(v);
+
+    fmprb_mul_2exp_si(t, x, 1);
+    fmpr_get_fmpz(v, fmprb_midref(t), FMPR_RND_NEAR);
+    fmprb_sub_fmpz(t, t, v, prec);
+
+    fmprb_const_pi(u, prec);
+    fmprb_mul(t, t, u, prec);
+    fmprb_mul_2exp_si(t, t, -1);
+
+    switch (fmpz_fdiv_ui(v, 4))
+    {
+        case 0:
+            fmprb_sin(y, t, prec);
+            break;
+        case 1:
+            fmprb_cos(y, t, prec);
+            break;
+        case 2:
+            fmprb_sin(y, t, prec);
+            fmprb_neg(y, y);
+            break;
+        default:
+            fmprb_cos(y, t, prec);
+            fmprb_neg(y, y);
+            break;
+    }
+
+    fmpz_clear(v);
+    fmprb_clear(t);
+    fmprb_clear(u);
+}
+
+void
+fmprb_cos_pi(fmprb_t y, const fmprb_t x, long prec)
+{
+    fmprb_t t;
+    fmprb_t u;
+    fmpz_t v;
+
+    fmprb_init(t);
+    fmprb_init(u);
+    fmpz_init(v);
+
+    fmprb_mul_2exp_si(t, x, 1);
+    fmpr_get_fmpz(v, fmprb_midref(t), FMPR_RND_NEAR);
+    fmprb_sub_fmpz(t, t, v, prec);
+
+    fmprb_const_pi(u, prec);
+    fmprb_mul(t, t, u, prec);
+    fmprb_mul_2exp_si(t, t, -1);
+
+    switch (fmpz_fdiv_ui(v, 4))
+    {
+        case 0:
+            fmprb_cos(y, t, prec);
+            break;
+        case 1:
+            fmprb_sin(y, t, prec);
+            fmprb_neg(y, y);
+            break;
+        case 2:
+            fmprb_cos(y, t, prec);
+            fmprb_neg(y, y);
+            break;
+        default:
+            fmprb_sin(y, t, prec);
+            break;
+    }
+
+    fmpz_clear(v);
+    fmprb_clear(t);
+    fmprb_clear(u);
+}
+
+void
+fmprb_sin_cos_pi(fmprb_t s, fmprb_t c, const fmprb_t x, long prec)
+{
+    fmprb_t t;
+    fmprb_t u;
+    fmpz_t v;
+
+    fmprb_init(t);
+    fmprb_init(u);
+    fmpz_init(v);
+
+    fmprb_mul_2exp_si(t, x, 1);
+    fmpr_get_fmpz(v, fmprb_midref(t), FMPR_RND_NEAR);
+    fmprb_sub_fmpz(t, t, v, prec);
+
+    fmprb_const_pi(u, prec);
+    fmprb_mul(t, t, u, prec);
+    fmprb_mul_2exp_si(t, t, -1);
+
+    switch (fmpz_fdiv_ui(v, 4))
+    {
+        case 0:
+            fmprb_sin_cos(s, c, t, prec);
+            break;
+        case 1:
+            fmprb_sin_cos(c, s, t, prec);
+            fmprb_neg(c, c);
+            break;
+        case 2:
+            fmprb_sin_cos(s, c, t, prec);
+            fmprb_neg(s, s);
+            fmprb_neg(c, c);
+            break;
+        default:
+            fmprb_sin_cos(c, s, t, prec);
+            fmprb_neg(s, s);
+            break;
+    }
+
+    fmpz_clear(v);
+    fmprb_clear(t);
+    fmprb_clear(u);
+}
+
diff --git a/fmprb/test/t-cos_pi.c b/fmprb/test/t-cos_pi.c
new file mode 100644
index 00000000..d12508b2
--- /dev/null
+++ b/fmprb/test/t-cos_pi.c
@@ -0,0 +1,76 @@
+/*=============================================================================
+
+    This file is part of ARB.
+
+    ARB is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    ARB is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License
+    along with ARB; if not, write to the Free Software
+    Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
+
+=============================================================================*/
+/******************************************************************************
+
+    Copyright (C) 2012, 2013 Fredrik Johansson
+
+******************************************************************************/
+
+#include "fmprb.h"
+
+int main()
+{
+    long iter;
+    flint_rand_t state;
+
+    printf("cos_pi....");
+    fflush(stdout);
+
+    flint_randinit(state);
+
+    for (iter = 0; iter < 1000; iter++)
+    {
+        fmprb_t a, b, c;
+        long prec = 2 + n_randint(state, 200);
+
+        fmprb_init(a);
+        fmprb_init(b);
+        fmprb_init(c);
+
+        fmprb_randtest(a, state, 1 + n_randint(state, 200), 10);
+        fmprb_randtest(b, state, 1 + n_randint(state, 200), 10);
+        fmprb_randtest(c, state, 1 + n_randint(state, 200), 10);
+
+        fmprb_const_pi(b, prec);
+        fmprb_mul(b, b, a, prec);
+        fmprb_cos(b, b, prec);
+
+        fmprb_cos_pi(c, a, prec);
+
+        if (!fmprb_overlaps(b, c))
+        {
+            printf("FAIL: overlap\n\n");
+            printf("a = "); fmprb_print(a); printf("\n\n");
+            printf("b = "); fmprb_print(b); printf("\n\n");
+            printf("c = "); fmprb_print(c); printf("\n\n");
+            abort();
+        }
+
+        fmprb_clear(a);
+        fmprb_clear(b);
+        fmprb_clear(c);
+    }
+
+    flint_randclear(state);
+    _fmpz_cleanup();
+    printf("PASS\n");
+    return EXIT_SUCCESS;
+}
+
diff --git a/fmprb/test/t-sin_cos_pi.c b/fmprb/test/t-sin_cos_pi.c
new file mode 100644
index 00000000..99042ed6
--- /dev/null
+++ b/fmprb/test/t-sin_cos_pi.c
@@ -0,0 +1,84 @@
+/*=============================================================================
+
+    This file is part of ARB.
+
+    ARB is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    ARB is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License
+    along with ARB; if not, write to the Free Software
+    Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
+
+=============================================================================*/
+/******************************************************************************
+
+    Copyright (C) 2012, 2013 Fredrik Johansson
+
+******************************************************************************/
+
+#include "fmprb.h"
+
+int main()
+{
+    long iter;
+    flint_rand_t state;
+
+    printf("sin_cos_pi....");
+    fflush(stdout);
+
+    flint_randinit(state);
+
+    for (iter = 0; iter < 1000; iter++)
+    {
+        fmprb_t a, b, c, d, e;
+        long prec = 2 + n_randint(state, 200);
+
+        fmprb_init(a);
+        fmprb_init(b);
+        fmprb_init(c);
+        fmprb_init(d);
+        fmprb_init(e);
+
+        fmprb_randtest(a, state, 1 + n_randint(state, 200), 10);
+        fmprb_randtest(b, state, 1 + n_randint(state, 200), 10);
+        fmprb_randtest(c, state, 1 + n_randint(state, 200), 10);
+        fmprb_randtest(d, state, 1 + n_randint(state, 200), 10);
+        fmprb_randtest(e, state, 1 + n_randint(state, 200), 10);
+
+        fmprb_const_pi(b, prec);
+        fmprb_mul(b, b, a, prec);
+        fmprb_sin_cos(b, d, b, prec);
+
+        fmprb_sin_cos_pi(c, e, a, prec);
+
+        if (!fmprb_overlaps(b, c) || !fmprb_overlaps(d, e))
+        {
+            printf("FAIL: overlap\n\n");
+            printf("a = "); fmprb_print(a); printf("\n\n");
+            printf("b = "); fmprb_print(b); printf("\n\n");
+            printf("c = "); fmprb_print(c); printf("\n\n");
+            printf("d = "); fmprb_print(d); printf("\n\n");
+            printf("e = "); fmprb_print(e); printf("\n\n");
+            abort();
+        }
+
+        fmprb_clear(a);
+        fmprb_clear(b);
+        fmprb_clear(c);
+        fmprb_clear(d);
+        fmprb_clear(e);
+    }
+
+    flint_randclear(state);
+    _fmpz_cleanup();
+    printf("PASS\n");
+    return EXIT_SUCCESS;
+}
+
diff --git a/fmprb/test/t-sin_pi.c b/fmprb/test/t-sin_pi.c
new file mode 100644
index 00000000..fdbbfb51
--- /dev/null
+++ b/fmprb/test/t-sin_pi.c
@@ -0,0 +1,76 @@
+/*=============================================================================
+
+    This file is part of ARB.
+
+    ARB is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    ARB is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License
+    along with ARB; if not, write to the Free Software
+    Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
+
+=============================================================================*/
+/******************************************************************************
+
+    Copyright (C) 2012, 2013 Fredrik Johansson
+
+******************************************************************************/
+
+#include "fmprb.h"
+
+int main()
+{
+    long iter;
+    flint_rand_t state;
+
+    printf("sin_pi....");
+    fflush(stdout);
+
+    flint_randinit(state);
+
+    for (iter = 0; iter < 1000; iter++)
+    {
+        fmprb_t a, b, c;
+        long prec = 2 + n_randint(state, 200);
+
+        fmprb_init(a);
+        fmprb_init(b);
+        fmprb_init(c);
+
+        fmprb_randtest(a, state, 1 + n_randint(state, 200), 10);
+        fmprb_randtest(b, state, 1 + n_randint(state, 200), 10);
+        fmprb_randtest(c, state, 1 + n_randint(state, 200), 10);
+
+        fmprb_const_pi(b, prec);
+        fmprb_mul(b, b, a, prec);
+        fmprb_sin(b, b, prec);
+
+        fmprb_sin_pi(c, a, prec);
+
+        if (!fmprb_overlaps(b, c))
+        {
+            printf("FAIL: overlap\n\n");
+            printf("a = "); fmprb_print(a); printf("\n\n");
+            printf("b = "); fmprb_print(b); printf("\n\n");
+            printf("c = "); fmprb_print(c); printf("\n\n");
+            abort();
+        }
+
+        fmprb_clear(a);
+        fmprb_clear(b);
+        fmprb_clear(c);
+    }
+
+    flint_randclear(state);
+    _fmpz_cleanup();
+    printf("PASS\n");
+    return EXIT_SUCCESS;
+}
+