Trigonometric Function Triangle Calculator

Trigonometric Formulas:

\[ \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \] \[ \cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} \] \[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \]

Angle (θ):

degrees

Opposite Side:

meters

Adjacent Side:

meters

Hypotenuse:

meters

Sine (sin θ):

Cosine (cos θ):

Tangent (tan θ):

Opposite Side:

Adjacent Side:

Hypotenuse:

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1. What is a Trigonometric Function Calculator?

Definition: This calculator computes the trigonometric functions (sine, cosine, tangent) for angles in a right triangle and can calculate missing sides.

Purpose: It helps students, engineers, and professionals solve right triangle problems in mathematics, physics, and engineering.

2. How Does the Calculator Work?

The calculator uses the fundamental trigonometric formulas:

\[ \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \] \[ \cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} \] \[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \]

Where:

\( \theta \) — Angle in degrees (0° to 90°)
opposite — Side opposite to angle θ
adjacent — Side adjacent to angle θ
hypotenuse — Longest side of the right triangle

Explanation: Enter any angle and at least two sides to calculate all trigonometric functions and missing sides.

3. Importance of Trigonometric Calculations

Details: Trigonometric functions are essential for solving problems involving right triangles, which appear in construction, navigation, physics, and engineering.

4. Using the Calculator

Tips:

Enter the angle in degrees (0-90)
Provide at least two of the three sides (opposite, adjacent, hypotenuse)
The calculator will compute all trigonometric functions and missing sides
Results are shown with 6 decimal places for functions and 3 for lengths

5. Frequently Asked Questions (FAQ)

Q1: What if I only know one side?
A: You need to know at least two sides plus the angle to calculate the remaining values.

Q2: Why are my calculated sides not matching?
A: The values must satisfy the Pythagorean theorem (a² + b² = c²). Check your inputs for consistency.

Q3: Can I use this for non-right triangles?
A: No, these formulas only work for right triangles. For other triangles, use the Law of Sines or Cosines.

Q4: What's the precision of the calculations?
A: Trigonometric functions are shown to 6 decimal places, side lengths to 3 decimal places.

Q5: How do I convert between degrees and radians?
A: 180° = π radians. The calculator automatically converts degrees to radians for calculations.