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Interactive Trigonometric Equations Visualization
Welcome to the Trigonometric Equations Explorer
This interactive visualization helps you understand how to solve trigonometric equations by finding where the function intersects with a target value. Explore different types of equations and see how periodicity creates multiple solutions.
What you can explore:
- Basic sine equations - sin(x) = k with two solutions per period
- Basic cosine equations - cos(x) = k with two solutions per period
- Basic tangent equations - tan(x) = k with one solution per period
- Squared equations - sin²(x) and cos²(x) with four solutions per period
- Linear combinations - More complex equations with transformations
How to Use This Visualization
Interactive Features:
- • Select Equation Type - Choose from 6 different trigonometric equations
- • Adjust Periods - Control how many periods to display
- • Toggle Visualizations - Show/hide solutions, target line, and intersections
- • View Solutions - See all solutions in the visible domain
What You'll See:
- • Function Curve (colored) - The trigonometric function
- • Target Line (red, dashed) - The value we're solving for
- • Solution Points (green) - Where function equals target value
- • Vertical Lines (green, dashed) - Connect solutions to x-axis
- • Solution List - All solutions with exact and decimal values
Basic sine equation with two solutions per period
More periods show more solutions
Solutions
x1
0.524
≈ 0.524
x2
2.618
≈ 2.618
x3
6.807
≈ 6.807
x4
8.901
≈ 8.901
x5
13.090
≈ 13.090
x6
15.184
≈ 15.184
Total: 6 solutions
Equation Info
Equation: sin(x) = 0.5
Target: 0.5
Periods: 4
Solving Strategy
Step 1: Isolate the trigonometric function (sin, cos, or tan).
Step 2: Find the reference angle using inverse trigonometric functions.
Step 3: Determine all solutions in one period using symmetry.
Step 4: Add period multiples to find all solutions: x = base + n·period.
Key Concepts
Periodicity: sin and cos have period 2π, tan has period π. Solutions repeat every period.
Multiple Solutions: Most trigonometric equations have infinitely many solutions due to periodicity.
General Solution: Express solutions as x = base + n·period where n is any integer.
General Solution Formulas
For sin(x) = k:
x = arcsin(k) + 2nπ
x = π - arcsin(k) + 2nπ
For cos(x) = k:
x = arccos(k) + 2nπ
x = -arccos(k) + 2nπ
For tan(x) = k:
x = arctan(k) + nπ
수업
개별 학습 단위
수업 준비 중