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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"]
]
)
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