diff --git a/complex.c b/complex.c
index 2a37c42126..95b1abbd45 100644
--- a/complex.c
+++ b/complex.c
@@ -661,8 +661,9 @@ f_complex_polar(VALUE klass, VALUE x, VALUE y)
 	    y = DBL2NUM(imag);
 	}
 	else {
-	    y = f_mul(x, DBL2NUM(sin(arg)));
-	    x = f_mul(x, DBL2NUM(cos(arg)));
+            const double ax = sin(arg), ay = cos(arg);
+            y = f_mul(x, DBL2NUM(ax));
+            x = f_mul(x, DBL2NUM(ay));
 	    if (canonicalization && f_zero_p(y)) return x;
 	}
 	return nucomp_s_new_internal(klass, x, y);
@@ -672,6 +673,16 @@ f_complex_polar(VALUE klass, VALUE x, VALUE y)
 					  f_mul(x, m_sin(y)));
 }
 
+#ifdef HAVE___COSPI
+# define cospi(x) __cospi(x)
+#else
+# define cospi(x) cos((x) * M_PI)
+#endif
+#ifdef HAVE___SINPI
+# define sinpi(x) __sinpi(x)
+#else
+# define sinpi(x) sin((x) * M_PI)
+#endif
 /* returns a Complex or Float of ang*PI-rotated abs */
 VALUE
 rb_dbl_complex_new_polar_pi(double abs, double ang)
@@ -689,8 +700,8 @@ rb_dbl_complex_new_polar_pi(double abs, double ang)
 	return DBL2NUM(abs);
     }
     else {
-	ang *= M_PI;
-	return rb_complex_new(DBL2NUM(abs * cos(ang)), DBL2NUM(abs * sin(ang)));
+        const double real = abs * cospi(ang), imag = abs * sinpi(ang);
+        return rb_complex_new(DBL2NUM(real), DBL2NUM(imag));
     }
 }
 
diff --git a/configure.ac b/configure.ac
index e16c3e44ed..f78eb38c93 100644
--- a/configure.ac
+++ b/configure.ac
@@ -1991,6 +1991,8 @@ AC_CHECK_FUNCS(utimensat)
 AC_CHECK_FUNCS(utimes)
 AC_CHECK_FUNCS(wait4)
 AC_CHECK_FUNCS(waitpid)
+AC_CHECK_FUNCS(__cospi)
+AC_CHECK_FUNCS(__sinpi)
 
 AS_IF([test "x$ac_cv_member_struct_statx_stx_btime" = xyes],
     [AC_CHECK_FUNCS(statx)])