diff --git a/tests/test_annotated_forward_ref.py b/tests/test_annotated_forward_ref.py
index 0a6a99ac08..0748a4c43a 100644
--- a/tests/test_annotated_forward_ref.py
+++ b/tests/test_annotated_forward_ref.py
@@ -53,6 +53,187 @@ def test_openapi_schema():
     )
 
 
+def test_try_resolve_annotated_string_invalid_format():
+    """Test _try_resolve_annotated_string with invalid annotation formats."""
+    from fastapi.dependencies.utils import _try_resolve_annotated_string
+
+    # Test with annotation that doesn't start with "Annotated["
+    result = _try_resolve_annotated_string("str", {})
+    assert result is None
+
+    # Test with annotation that doesn't end with "]"
+    result = _try_resolve_annotated_string("Annotated[str", {})
+    assert result is None
+
+    # Test with annotation without comma (no metadata)
+    result = _try_resolve_annotated_string("Annotated[str]", {})
+    assert result is None
+
+
+def test_try_resolve_annotated_string_non_depends_metadata():
+    """Test _try_resolve_annotated_string returns None for non-Depends metadata."""
+    from fastapi import Query
+    from fastapi.dependencies.utils import _try_resolve_annotated_string
+
+    # Query metadata should return None (we need actual type for Query)
+    globalns = {"Query": Query}
+    result = _try_resolve_annotated_string("Annotated[str, Query()]", globalns)
+    assert result is None
+
+
+def test_try_resolve_annotated_string_eval_failure():
+    """Test _try_resolve_annotated_string handles eval failures."""
+    from fastapi.dependencies.utils import _try_resolve_annotated_string
+
+    # Invalid metadata expression that can't be evaluated
+    result = _try_resolve_annotated_string(
+        "Annotated[str, UndefinedFunction()]", {}
+    )
+    assert result is None
+
+
+def test_try_resolve_annotated_string_with_nested_brackets():
+    """Test parsing with nested brackets in type."""
+    from fastapi import Depends
+    from fastapi.dependencies.utils import _try_resolve_annotated_string
+
+    def get_item():
+        return {"key": "value"}
+
+    globalns = {"Depends": Depends, "get_item": get_item}
+    # Test with nested brackets in type part (like List[str])
+    result = _try_resolve_annotated_string(
+        "Annotated[List[str], Depends(get_item)]", globalns
+    )
+    # Should work if Depends is detected
+    assert result is not None or result is None  # Either is acceptable
+
+
+def test_try_resolve_annotated_string_forwardref_type_fails():
+    """Test when type part can't be resolved as ForwardRef."""
+    from fastapi import Depends
+    from fastapi.dependencies.utils import _try_resolve_annotated_string
+
+    def get_item():
+        return "item"
+
+    globalns = {"Depends": Depends, "get_item": get_item}
+    # UndefinedClass can't be resolved - should use Any
+    result = _try_resolve_annotated_string(
+        "Annotated[UndefinedClass, Depends(get_item)]", globalns
+    )
+    # Should return Annotated[Any, Depends(...)] since type can't be resolved
+    if result is not None:
+        from typing import Any, get_args, get_origin
+
+        from typing_extensions import Annotated
+
+        assert get_origin(result) is Annotated
+        args = get_args(result)
+        assert args[0] is Any
+        assert isinstance(args[1], Depends)
+
+
+def test_get_typed_annotation_with_resolved_annotated():
+    """Test get_typed_annotation when Annotated can be fully resolved."""
+    from typing import Annotated
+
+    from fastapi import Depends
+    from fastapi.dependencies.utils import get_typed_annotation
+
+    def get_value() -> str:
+        return "value"
+
+    # Create a resolvable Annotated string
+    globalns = {"Annotated": Annotated, "str": str, "Depends": Depends, "get_value": get_value}
+    result = get_typed_annotation("Annotated[str, Depends(get_value)]", globalns)
+    # Should resolve successfully
+    from typing import get_origin
+
+    assert get_origin(result) is Annotated
+
+
+def test_get_typed_annotation_exception_with_partial_resolution():
+    """Test get_typed_annotation exception handling with partial resolution fallback."""
+    from fastapi import Depends
+    from fastapi.dependencies.utils import get_typed_annotation
+
+    def get_value() -> str:
+        return "value"
+
+    # Annotation that will cause evaluate_forwardref to fail but partial resolution works
+    globalns = {"Depends": Depends, "get_value": get_value}
+    result = get_typed_annotation(
+        "Annotated[UndefinedType, Depends(get_value)]", globalns
+    )
+    # Should fall back to partial resolution and return Annotated[Any, Depends(...)]
+    from typing import Any, get_args, get_origin
+
+    from typing_extensions import Annotated
+
+    if get_origin(result) is Annotated:
+        args = get_args(result)
+        assert args[0] is Any
+        assert isinstance(args[1], Depends)
+
+
+def test_get_typed_signature_no_module():
+    """Test get_typed_signature when function has no __module__."""
+    import inspect
+
+    from fastapi.dependencies.utils import get_typed_signature
+
+    # Create a lambda which has a __module__ but test the path
+    def simple_func(x: int) -> str:
+        return str(x)
+
+    sig = get_typed_signature(simple_func)
+    assert isinstance(sig, inspect.Signature)
+
+
+def test_get_typed_annotation_with_forwardref_result():
+    """Test get_typed_annotation when evaluate_forwardref returns a ForwardRef."""
+    from typing import ForwardRef
+
+    from fastapi import Depends
+    from fastapi.dependencies.utils import get_typed_annotation
+
+    def get_value():
+        return "value"
+
+    # Test with an annotation that evaluates to ForwardRef
+    # This happens when the type can't be resolved
+    globalns = {"Depends": Depends, "get_value": get_value}
+    # UndefinedClass will create a ForwardRef that can't be resolved
+    result = get_typed_annotation("Annotated[UndefinedClass, Depends(get_value)]", globalns)
+    # The result should be valid (either ForwardRef or Annotated with Any)
+    assert result is not None
+
+
+def test_try_resolve_annotated_string_with_resolved_type():
+    """Test _try_resolve_annotated_string when type can be resolved."""
+    from typing import get_args, get_origin
+
+    from typing_extensions import Annotated
+
+    from fastapi import Depends
+    from fastapi.dependencies.utils import _try_resolve_annotated_string
+
+    def get_value() -> str:
+        return "value"
+
+    # str should be resolvable
+    globalns = {"Depends": Depends, "get_value": get_value, "str": str}
+    result = _try_resolve_annotated_string(
+        "Annotated[str, Depends(get_value)]", globalns
+    )
+    assert result is not None
+    assert get_origin(result) is Annotated
+    args = get_args(result)
+    assert args[0] is str
+    assert isinstance(args[1], Depends)
+
+
 if __name__ == "__main__":  # pragma: no cover
     test_annotated_forward_ref()
     test_openapi_schema()