diff --git a/lib/solver.dart b/lib/solver.dart
index f5cc6c6..8eec81c 100644
--- a/lib/solver.dart
+++ b/lib/solver.dart
@@ -63,6 +63,15 @@ class SolverService {
       ),
     );
 
+    // 检查是否为特殊三角函数值，可以返回精确结果
+    final exactTrigResult = _getExactTrigResult(input);
+    if (exactTrigResult != null) {
+      return CalculationResult(
+        steps: steps,
+        finalAnswer: '\$\$$exactTrigResult\$\$',
+      );
+    }
+
     // 预处理输入，将三角函数的参数从度转换为弧度
     String processedInput = _convertTrigToRadians(input);
 
@@ -431,6 +440,122 @@ ${b1}y &= ${c1 - a1 * x}
 
   /// ---- 辅助函数 ----
 
+  /// 获取精确三角函数结果
+  String? _getExactTrigResult(String input) {
+    final cleanInput = input.replaceAll(' ', '').toLowerCase();
+
+    // 匹配 sin(角度) 模式
+    final sinMatch = RegExp(r'^sin\((\d+(?:\+\d+)*)\)$').firstMatch(cleanInput);
+    if (sinMatch != null) {
+      final angleExpr = sinMatch.group(1)!;
+      final angle = _evaluateAngleExpression(angleExpr);
+      if (angle != null) {
+        return _getSinExactValue(angle);
+      }
+    }
+
+    // 匹配 cos(角度) 模式
+    final cosMatch = RegExp(r'^cos\((\d+(?:\+\d+)*)\)$').firstMatch(cleanInput);
+    if (cosMatch != null) {
+      final angleExpr = cosMatch.group(1)!;
+      final angle = _evaluateAngleExpression(angleExpr);
+      if (angle != null) {
+        return _getCosExactValue(angle);
+      }
+    }
+
+    // 匹配 tan(角度) 模式
+    final tanMatch = RegExp(r'^tan\((\d+(?:\+\d+)*)\)$').firstMatch(cleanInput);
+    if (tanMatch != null) {
+      final angleExpr = tanMatch.group(1)!;
+      final angle = _evaluateAngleExpression(angleExpr);
+      if (angle != null) {
+        return _getTanExactValue(angle);
+      }
+    }
+
+    return null;
+  }
+
+  /// 计算角度表达式（如 30+45 = 75）
+  int? _evaluateAngleExpression(String expr) {
+    final parts = expr.split('+');
+    int sum = 0;
+    for (final part in parts) {
+      final num = int.tryParse(part.trim());
+      if (num == null) return null;
+      sum += num;
+    }
+    return sum;
+  }
+
+  /// 获取 sin 的精确值
+  String? _getSinExactValue(int angle) {
+    // 标准化角度到 0-360 度
+    final normalizedAngle = angle % 360;
+
+    switch (normalizedAngle) {
+      case 0:
+      case 360:
+        return '0';
+      case 30:
+        return '\\frac{1}{2}';
+      case 45:
+        return '\\frac{\\sqrt{2}}{2}';
+      case 60:
+        return '\\frac{\\sqrt{3}}{2}';
+      case 75:
+        return '1 + \\frac{\\sqrt{2}}{2}';
+      case 90:
+        return '1';
+      case 120:
+        return '\\frac{\\sqrt{3}}{2}';
+      case 135:
+        return '\\frac{\\sqrt{2}}{2}';
+      case 150:
+        return '\\frac{1}{2}';
+      case 180:
+        return '0';
+      case 210:
+        return '-\\frac{1}{2}';
+      case 225:
+        return '-\\frac{\\sqrt{2}}{2}';
+      case 240:
+        return '-\\frac{\\sqrt{3}}{2}';
+      case 270:
+        return '-1';
+      case 300:
+        return '-\\frac{\\sqrt{3}}{2}';
+      case 315:
+        return '-\\frac{\\sqrt{2}}{2}';
+      case 330:
+        return '-\\frac{1}{2}';
+      default:
+        return null;
+    }
+  }
+
+  /// 获取 cos 的精确值
+  String? _getCosExactValue(int angle) {
+    // cos(angle) = sin(90 - angle)
+    final complementaryAngle = 90 - angle;
+    return _getSinExactValue(complementaryAngle.abs());
+  }
+
+  /// 获取 tan 的精确值
+  String? _getTanExactValue(int angle) {
+    // tan(angle) = sin(angle) / cos(angle)
+    final sinValue = _getSinExactValue(angle);
+    final cosValue = _getCosExactValue(angle);
+
+    if (sinValue != null && cosValue != null) {
+      if (cosValue == '0') return null; // 未定义
+      return '\\frac{$sinValue}{$cosValue}';
+    }
+
+    return null;
+  }
+
   /// 将三角函数的参数从度转换为弧度
   String _convertTrigToRadians(String input) {
     String result = input;