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| import math | |
| import gradio as gr | |
| def solve_trig_equations(a: float, b: float, c: float, trig_func: str, interval_degrees: tuple[float, float] = (0, 360)) -> str: | |
| """ | |
| Solves basic trigonometric equations of the form a * func(x) + b = c. | |
| Finds solutions for x within a given interval (in degrees). | |
| Args: | |
| a: Coefficient of the trigonometric function. | |
| b: Constant term added to the function part. | |
| c: Constant term on the other side of the equation. | |
| trig_func: The trigonometric function ("sin", "cos", "tan"). | |
| interval_degrees: Tuple (min_angle, max_angle) for solutions in degrees. | |
| Returns: | |
| A string describing the solutions in degrees. | |
| """ | |
| if a == 0: | |
| return "Error: Coefficient 'a' cannot be zero." | |
| val = (c - b) / a | |
| func = trig_func.lower() | |
| solutions_deg = [] | |
| if func == "sin": | |
| if not (-1 <= val <= 1): | |
| return f"No solution: sin(x) cannot be {val:.4f}." | |
| angle_rad_principal = math.asin(val) | |
| elif func == "cos": | |
| if not (-1 <= val <= 1): | |
| return f"No solution: cos(x) cannot be {val:.4f}." | |
| angle_rad_principal = math.acos(val) | |
| elif func == "tan": | |
| angle_rad_principal = math.atan(val) | |
| else: | |
| return "Error: Invalid trigonometric function. Choose 'sin', 'cos', or 'tan'." | |
| angle_deg_principal = math.degrees(angle_rad_principal) | |
| min_interval_deg, max_interval_deg = interval_degrees | |
| for n in range(int(min_interval_deg / 360) - 2, int(max_interval_deg / 360) + 3): | |
| if func == "sin": | |
| sol1_deg = n * 360 + angle_deg_principal | |
| sol2_deg = n * 360 + (180 - angle_deg_principal) | |
| if min_interval_deg <= sol1_deg <= max_interval_deg: | |
| solutions_deg.append(sol1_deg) | |
| if min_interval_deg <= sol2_deg <= max_interval_deg: | |
| solutions_deg.append(sol2_deg) | |
| elif func == "cos": | |
| sol1_deg = n * 360 + angle_deg_principal | |
| sol2_deg = n * 360 - angle_deg_principal | |
| if min_interval_deg <= sol1_deg <= max_interval_deg: | |
| solutions_deg.append(sol1_deg) | |
| if min_interval_deg <= sol2_deg <= max_interval_deg: | |
| solutions_deg.append(sol2_deg) | |
| elif func == "tan": | |
| for n_tan in range(int(min_interval_deg / 180) - 2, int(max_interval_deg / 180) + 3): | |
| sol_deg = n_tan * 180 + angle_deg_principal | |
| if min_interval_deg <= sol_deg <= max_interval_deg: | |
| solutions_deg.append(sol_deg) | |
| unique_solutions = sorted(list(set(f"{s:.2f}" for s in solutions_deg))) | |
| if not unique_solutions: | |
| return f"No solutions found for {a}*{func}(x) + {b} = {c} in the interval [{min_interval_deg}, {max_interval_deg}] degrees." | |
| return f"Solutions for x in [{min_interval_deg}, {max_interval_deg}] degrees: {', '.join(unique_solutions)}" | |
| def parse_interval(interval_str: str) -> tuple[float, float]: | |
| try: | |
| parts = [float(x.strip()) for x in interval_str.split(',')] | |
| if len(parts) == 2 and parts[0] <= parts[1]: | |
| return parts[0], parts[1] | |
| raise ValueError("Interval must be two numbers, min,max.") | |
| except Exception: | |
| raise gr.Error("Invalid interval format. Use 'min,max' (e.g., '0,360').") | |
| solve_trig_equations_interface = gr.Interface( | |
| fn=lambda a, b, c, func, interval_str: solve_trig_equations(a, b, c, func, parse_interval(interval_str)), | |
| inputs=[ | |
| gr.Number(label="a (coefficient of function)"), | |
| gr.Number(label="b (constant added to function part)"), | |
| gr.Number(label="c (constant on other side of equation)"), | |
| gr.Radio(["sin", "cos", "tan"], label="Trigonometric Function"), | |
| gr.Textbox(label="Interval for x (degrees, comma-separated, e.g., 0,360)", value="0,360") | |
| ], | |
| outputs="text", | |
| title="Trigonometric Equation Solver", | |
| description="Solves equations like a * func(x) + b = c for x in a given interval (degrees). Enter the coefficients, select the function, and specify the interval for x. Example: Solve 2*sin(x) + 1 = 1 for x in [0,360] degrees.", | |
| examples=[ | |
| [2, 1, 1, "sin", "0,360"], | |
| [1, 0, 0.5, "cos", "0,360"], | |
| [1, 0, 1, "tan", "0,360"], | |
| [1, 0, 2, "sin", "0,360"] | |
| ] | |
| ) | |