diff --git a/source/maths/Fixed.cpp b/source/maths/Fixed.cpp
index 76d9941467..445985e926 100644
--- a/source/maths/Fixed.cpp
+++ b/source/maths/Fixed.cpp
@@ -133,8 +133,51 @@ CFixed_15_16 CFixed_15_16::Pi()
 
 void sincos_approx(CFixed_15_16 a, CFixed_15_16& sin_out, CFixed_15_16& cos_out)
 {
-	// XXX: mustn't use floating-point here - need a fixed-point emulation
+	// Based on http://www.coranac.com/2009/07/sines/
 
-	sin_out = CFixed_15_16::FromDouble(sin(a.ToDouble()));
-	cos_out = CFixed_15_16::FromDouble(cos(a.ToDouble()));
+	// TODO: this could be made a bit more precise by being careful about scaling
+
+	typedef CFixed_15_16 fixed;
+
+	fixed c2_pi;
+	c2_pi.SetInternalValue(41721); // = 2/pi << 16
+
+	// Map radians onto the range [0, 4)
+	fixed z = a.Multiply(c2_pi) % fixed::FromInt(4);
+
+	// Map z onto the range [-1, +1] for sin, and the same with z+1 to compute cos
+	fixed sz, cz;
+	if (z >= fixed::FromInt(3)) // [3, 4)
+	{
+		sz = z - fixed::FromInt(4);
+		cz = z - fixed::FromInt(3);
+	}
+	else if (z >= fixed::FromInt(2)) // [2, 3)
+	{
+		sz = fixed::FromInt(2) - z;
+		cz = z - fixed::FromInt(3);
+	}
+	else if (z >= fixed::FromInt(1)) // [1, 2)
+	{
+		sz = fixed::FromInt(2) - z;
+		cz = fixed::FromInt(1) - z;
+	}
+	else // [0, 1)
+	{
+		sz = z;
+		cz = fixed::FromInt(1) - z;
+	}
+
+	// Third-order (max absolute error ~0.02)
+
+//	sin_out = (sz / 2).Multiply(fixed::FromInt(3) - sz.Multiply(sz));
+//	cos_out = (cz / 2).Multiply(fixed::FromInt(3) - cz.Multiply(cz));
+
+	// Fifth-order (max absolute error ~0.0005)
+
+	fixed sz2 = sz.Multiply(sz);
+	sin_out = sz.Multiply(fixed::Pi() - sz2.Multiply(fixed::Pi()*2 - fixed::FromInt(5) - sz2.Multiply(fixed::Pi() - fixed::FromInt(3)))) / 2;
+
+	fixed cz2 = cz.Multiply(cz);
+	cos_out = cz.Multiply(fixed::Pi() - cz2.Multiply(fixed::Pi()*2 - fixed::FromInt(5) - cz2.Multiply(fixed::Pi() - fixed::FromInt(3)))) / 2;
 }
diff --git a/source/maths/Fixed.h b/source/maths/Fixed.h
index 2a07e429f6..859fba99c3 100644
--- a/source/maths/Fixed.h
+++ b/source/maths/Fixed.h
@@ -234,6 +234,18 @@ public:
 		return CFixed(value / n);
 	}
 
+	/// Mod by a fixed. Must not have n == 0. Result has the same sign as n.
+	CFixed operator%(CFixed n) const
+	{
+		T t = value % n.value;
+		if (n.value > 0 && t < 0)
+			t += n.value;
+		else if (n.value < 0 && t > 0)
+			t += n.value;
+
+		return CFixed(t);
+	}
+
 	CFixed Absolute() const { return CFixed(abs(value)); }
 
 	/**
@@ -307,6 +319,7 @@ CFixed_15_16 atan2_approx(CFixed_15_16 y, CFixed_15_16 x);
 
 /**
  * Compute sin(a) and cos(a).
+ * Maximum error for -2pi < a < 2pi is almost 0.0005.
  */
 void sincos_approx(CFixed_15_16 a, CFixed_15_16& sin_out, CFixed_15_16& cos_out);
 
diff --git a/source/maths/tests/test_Fixed.h b/source/maths/tests/test_Fixed.h
index ba4f85d2de..d78a628ccc 100644
--- a/source/maths/tests/test_Fixed.h
+++ b/source/maths/tests/test_Fixed.h
@@ -134,6 +134,20 @@ public:
 
 	// TODO: test all the arithmetic operators
 
+	void test_Mod()
+	{
+		TS_ASSERT_EQUALS(fixed::FromInt(0) % fixed::FromInt(4), fixed::FromInt(0));
+		TS_ASSERT_EQUALS(fixed::FromInt(0) % fixed::FromInt(-4), fixed::FromInt(0));
+		TS_ASSERT_EQUALS(fixed::FromInt(5) % fixed::FromInt(4), fixed::FromInt(1));
+		TS_ASSERT_EQUALS(fixed::FromInt(5) % fixed::FromInt(-4), fixed::FromInt(-3));
+		TS_ASSERT_EQUALS(fixed::FromInt(-5) % fixed::FromInt(4), fixed::FromInt(3));
+		TS_ASSERT_EQUALS(fixed::FromInt(-5) % fixed::FromInt(-4), fixed::FromInt(-1));
+
+		TS_ASSERT_EQUALS((fixed::FromDouble(5.5) % fixed::FromInt(4)).ToDouble(), 1.5);
+
+		TS_ASSERT_EQUALS((fixed::FromDouble(1.75) % fixed::FromDouble(0.5)).ToDouble(), 0.25);
+	}
+
 	void test_Sqrt()
 	{
 		TS_ASSERT_EQUALS(fixed::FromDouble(1.0).Sqrt().ToDouble(), 1.0);
@@ -188,4 +202,48 @@ public:
 
 		#undef T
 	}
+
+	void test_SinCos()
+	{
+		fixed s, c;
+
+		sincos_approx(fixed::FromInt(0), s, c);
+		TS_ASSERT_EQUALS(s, fixed::FromInt(0));
+		TS_ASSERT_EQUALS(c, fixed::FromInt(1));
+
+		sincos_approx(fixed::Pi(), s, c);
+		TS_ASSERT_DELTA(s.ToDouble(), 0.0, 0.00005);
+		TS_ASSERT_EQUALS(c, fixed::FromInt(-1));
+
+		sincos_approx(fixed::FromDouble(M_PI*2.0), s, c);
+		TS_ASSERT_DELTA(s.ToDouble(), 0.0, 0.0001);
+		TS_ASSERT_DELTA(c.ToDouble(), 1.0, 0.0001);
+
+		sincos_approx(fixed::FromDouble(M_PI*100.0), s, c);
+		TS_ASSERT_DELTA(s.ToDouble(), 0.0, 0.004);
+		TS_ASSERT_DELTA(c.ToDouble(), 1.0, 0.004);
+
+		sincos_approx(fixed::FromDouble(M_PI*-100.0), s, c);
+		TS_ASSERT_DELTA(s.ToDouble(), 0.0, 0.004);
+		TS_ASSERT_DELTA(c.ToDouble(), 1.0, 0.004);
+
+/*
+		for (double a = 0.0; a < 6.28; a += 0.1)
+		{
+			sincos_approx(fixed::FromDouble(a), s, c);
+			printf("%f: sin = %f / %f; cos = %f / %f\n", a, s.ToDouble(), sin(a), c.ToDouble(), cos(a));
+		}
+*/
+
+		double err = 0.0;
+		for (double a = -6.28; a < 6.28; a += 0.001)
+		{
+			sincos_approx(fixed::FromDouble(a), s, c);
+			err = std::max(err, fabs(sin(a) - s.ToDouble()));
+			err = std::max(err, fabs(cos(a) - c.ToDouble()));
+		}
+//		printf("### Max error %f = %f/2^16\n", err, err*65536.0);
+
+		TS_ASSERT_LESS_THAN(err, 0.00046);
+	}
 };