diff --git a/stencils/trigonometry.c b/stencils/trigonometry.c
index da995bd..927ec36 100644
--- a/stencils/trigonometry.c
+++ b/stencils/trigonometry.c
@@ -67,7 +67,7 @@ __attribute__((noinline)) float aux_cos(float x) {
     // Select function and sign based on quadrant
     int qm = q & 3;
     int use_sin = (qm == 1 || qm == 3);
-    int sign = (qm == 0 || qm == 1) ? +1 : -1;
+    int sign = (qm == 0 || qm == 3) ? +1 : -1;
 
     float r2 = r * r;
 
@@ -101,15 +101,15 @@ __attribute__((noinline)) float aux_tan(float x) {
     int q = (int)(qd + (qd >= 0.0 ? 0.5 : -0.5));  // nearest integer
 
     // Range reduce: r = x - q*(pi/2)
-    const double PIO2_HI = 1.57079625129699707031;     // π/2 high part
-    const double PIO2_LO = 7.54978941586159635335e-08; // π/2 low part
+    const double PIO2_HI = 1.57079625129699707031;     // pi/2 high part
+    const double PIO2_LO = 7.54978941586159635335e-08; // pi/2 low part
     double r_d = xd - (double)q * PIO2_HI - (double)q * PIO2_LO;
     float r = (float)r_d;
 
-    // For tan: period is π, so q mod 2 determines sign
+    // For tan: period is pi, so q mod 2 determines sign
     int qm = q & 3;
     int use_cot = (qm == 1 || qm == 3); // tan(x) = ±cot(r) in odd quadrants
-    int sign = (qm == 1 || qm == 2) ? -1 : +1;
+    int sign = (qm == 0 || qm == 2) ? +1 : -1;
 
     // Polynomial approximations
     // sin(r) ≈ r + s3*r^3 + s5*r^5 + s7*r^7 + s9*r^9
diff --git a/tests/test_math.py b/tests/test_math.py
index acc0d1d..3deaaa7 100644
--- a/tests/test_math.py
+++ b/tests/test_math.py
@@ -29,7 +29,6 @@ def test_corse():
         assert val == pytest.approx(ref, 2), f"Result does not match: {val} and reference: {ref}"  # pyright: ignore[reportUnknownMemberType]
 
 
-@pytest.mark.skip(reason="sqrt must be fixed")
 def test_fine():
     a_i = 9
     a_f = 2.5
@@ -37,8 +36,21 @@ def test_fine():
     c_f = variable(a_f)
     # c_b = variable(True)
 
-    ret_test = (c_f ** 2, c_i ** -1, cp.sqrt(c_i), cp.sqrt(c_f), cp.sin(c_f), cp.cos(c_f), cp.tan(c_f))  # , c_i & 3)
-    ret_refe = (a_f ** 2, a_i ** -1, cp.sqrt(a_i), cp.sqrt(a_f), cp.sin(a_f), cp.cos(a_f), cp.tan(a_f))  # , a_i & 3)
+    ret_test = (c_f ** 2,
+                c_i ** -1,
+                cp.sqrt(c_i),
+                cp.sqrt(c_f),
+                cp.sin(c_f),
+                cp.cos(c_f),
+                cp.tan(c_f))  # , c_i & 3)
+    
+    ret_refe = (a_f ** 2,
+                a_i ** -1,
+                cp.sqrt(a_i),
+                cp.sqrt(a_f),
+                cp.sin(a_f),
+                cp.cos(a_f),
+                cp.tan(a_f))  # , a_i & 3)
 
     tg = Target()
     print('* compile and copy ...')
@@ -47,13 +59,33 @@ def test_fine():
     tg.run()
     print('* finished')
 
-    for test, ref in zip(ret_test, ret_refe):
+    for test, ref, name in zip(ret_test, ret_refe, ('^2', '**-1', 'sqrt_int', 'sqrt_float', 'sin', 'cos', 'tan')):
         assert isinstance(test, cp.variable)
         val = tg.read_value(test)
         print('+', val, ref, type(val), test.dtype)
         #for t in (int, float, bool):
         #    assert isinstance(val, t) == isinstance(ref, t), f"Result type does not match for {val} and {ref}"
-        assert val == pytest.approx(ref, 0.001), f"Result does not match: {val} and reference: {ref}"  # pyright: ignore[reportUnknownMemberType]
+        assert val == pytest.approx(ref, 1e-5), f"Result  for {name} does not match: {val} and reference: {ref}"  # pyright: ignore[reportUnknownMemberType]
+
+
+def test_trig_precision():
+
+    test_vals = [0.0, 0.0001, 0.1, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0, 4.5, 5.0, 5.5, 6.0, 6.28318530718, 100.0, 1000.0, 100000.0]  # up to 2pi
+
+    ret_test = [r for v in test_vals for r in (cp.sin(variable(v)), cp.cos(variable(v)), cp.tan(variable(v)))]
+    ret_refe = [r for v in test_vals for r in (cp.sin(v), cp.cos(v), cp.tan(v))]
+
+
+    tg = Target()
+    tg.compile(ret_test)
+    tg.run()
+
+    for i, (test, ref) in enumerate(zip(ret_test, ret_refe)):
+        func_name = ['sin', 'cos', 'tan'][i % 3]
+        assert isinstance(test, cp.variable)
+        val = tg.read_value(test)
+        print(f"+ Result of {func_name}: {val}; reference: {ref}")
+        assert val == pytest.approx(ref, abs=1e-5), f"Result of {func_name} for input {test_vals[i // 3]} does not match: {val} and reference: {ref}"  # pyright: ignore[reportUnknownMemberType]
 
 
 if __name__ == "__main__":
diff --git a/tests/test_vector.py b/tests/test_vector.py
index 297551b..b448417 100644
--- a/tests/test_vector.py
+++ b/tests/test_vector.py
@@ -11,7 +11,7 @@ def test_vectors_init():
 
     print(tt1, tt2, tt3, tt4, tt5)
 
-@pytest.mark.skip(reason="sqrt must be fixed")
+
 def test_compiled_vectors():
     t1 = cp.vector([10, 11, 12]) + cp.vector(cp.variable(v) for v in range(3))
     t2 = t1.sum()