XXX fix _eval_is_rational helpers for inverse trig

Validation:

In[2]:= FullSimplify[ArcSin[x] \[Element] Rationals,
 Assumptions -> x != 0 && x \[Element] Rationals]

Out[2]= False

In[5]:= FullSimplify[ArcCos[x] \[Element] Rationals,
 Assumptions -> x != 1 && x \[Element] Rationals]

Out[5]= False

In[9]:= FullSimplify[ArcTan[x] \[Element] Rationals,
 Assumptions -> x != 0 && x \[Element] Rationals]

Out[9]= False

In[16]:= FullSimplify[ArcCot[x] \[Element] Rationals,
 Assumptions -> x \[Element] Rationals]

Out[16]= False

diofant/functions/elementary/tests/test_trigonometric.py

@@ -665,6 +665,15 @@ def test_asin():
     assert asin(-2).is_extended_real is False
     assert asin(r).is_extended_real is None
 
+    assert asin(0, evaluate=False).is_rational
+    assert asin(1, evaluate=False).is_rational is False
+
+    z = Symbol('z', zero=True)
+    rn = Symbol('rn', rational=True, nonzero=True)
+    assert asin(z).is_rational
+    assert asin(rn).is_rational is False
+    assert asin(x).is_rational is None
+
     assert asin(-2*I) == -I*asinh(2)
 
     assert asin(Rational(1, 7), evaluate=False).is_positive is True
@@ -712,6 +721,15 @@ def test_acos():
     assert acos(-2).is_extended_real is False
     assert acos(r).is_extended_real is None
 
+    assert acos(1, evaluate=False).is_rational
+    assert acos(0, evaluate=False).is_rational is False
+
+    z = Symbol('z', zero=True)
+    rn = Symbol('rn', rational=True, nonzero=True)
+    assert acos(1 + z).is_rational
+    assert acos(1 + rn).is_rational is False
+    assert acos(x).is_rational is None
+
     assert acos(Rational(1, 7), evaluate=False).is_positive is True
     assert acos(Rational(-1, 7), evaluate=False).is_positive is True
     assert acos(Rational(3, 2), evaluate=False).is_positive is False
@@ -766,6 +784,15 @@ def test_atan():
     assert atan(n).is_positive is False
     assert atan(x).is_positive is None
 
+    assert atan(0, evaluate=False).is_rational
+    assert atan(1, evaluate=False).is_rational is False
+
+    z = Symbol('z', zero=True)
+    rn = Symbol('rn', rational=True, nonzero=True)
+    assert atan(z).is_rational
+    assert atan(rn).is_rational is False
+    assert atan(x).is_rational is None
+
 
 def test_atan_rewrite():
     assert atan(x).rewrite(log) == I*log((1 - I*x)/(1 + I*x))/2
@@ -857,6 +884,13 @@ def test_acot():
     assert acot(p).is_positive is True
     assert acot(I).is_positive is False
 
+    assert acot(0, evaluate=False).is_rational is False
+
+    z = Symbol('z', zero=True)
+    rn = Symbol('rn', rational=True, nonzero=True)
+    assert acot(1 + rn).is_rational is False
+    assert acot(x).is_rational is None
+
 
 def test_acot_rewrite():
     assert acot(x).rewrite(log) == I*log((x - I)/(x + I))/2

diofant/functions/elementary/trigonometric.py

@@ -1510,7 +1510,9 @@ def fdiff(self, argindex=1):
     def _eval_is_rational(self):
         s = self.func(*self.args)
         if s.func == self.func:
-            if s.args[0].is_rational:
+            if s.args[0].is_zero:
+                return True
+            elif s.args[0].is_rational and s.args[0].is_nonzero:
                 return False
         else:
             return s.is_rational
@@ -1680,7 +1682,9 @@ def fdiff(self, argindex=1):
     def _eval_is_rational(self):
         s = self.func(*self.args)
         if s.func == self.func:
-            if s.args[0].is_rational:
+            if (s.args[0] - 1).is_zero:
+                return True
+            elif s.args[0].is_rational and (s.args[0] - 1).is_nonzero:
                 return False
         else:
             return s.is_rational
@@ -1845,7 +1849,9 @@ def fdiff(self, argindex=1):
     def _eval_is_rational(self):
         s = self.func(*self.args)
         if s.func == self.func:
-            if s.args[0].is_rational:
+            if s.args[0].is_zero:
+                return True
+            elif s.args[0].is_rational and s.args[0].is_nonzero:
                 return False
         else:
             return s.is_rational
@@ -1990,7 +1996,7 @@ def fdiff(self, argindex=1):
     def _eval_is_rational(self):
         s = self.func(*self.args)
         if s.func == self.func:
-            if s.args[0].is_rational:
+            if s.args[0].is_rational and (s.args[0] - 1).is_nonzero:
                 return False
         else:
             return s.is_rational