Trigonometric Ratios Calculator

Trigonometric Ratios:

\[ \sin(\theta) = \frac{\text{Opposite}}{\text{Hypotenuse}} \] \[ \cos(\theta) = \frac{\text{Adjacent}}{\text{Hypotenuse}} \] \[ \tan(\theta) = \frac{\text{Opposite}}{\text{Adjacent}} \]

Opposite:

meters

Adjacent:

meters

Hypotenuse:

meters

Angle (θ):

degrees

Results:

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1. What Are Trigonometric Ratios?

Trigonometric ratios relate the angles of a right triangle to the lengths of its sides. The three primary ratios are sine (sin), cosine (cos), and tangent (tan).

2. How Does the Calculator Work?

The calculator computes trigonometric ratios using the following formulas:

\[ \sin(\theta) = \frac{\text{Opposite}}{\text{Hypotenuse}} \] \[ \cos(\theta) = \frac{\text{Adjacent}}{\text{Hypotenuse}} \] \[ \tan(\theta) = \frac{\text{Opposite}}{\text{Adjacent}} \]

Where:

Opposite — Side opposite to angle θ
Adjacent — Side adjacent to angle θ
Hypotenuse — Longest side of the right triangle
θ — Angle in degrees

3. Applications of Trigonometric Ratios

Details: Trigonometric ratios are fundamental in geometry, physics, engineering, navigation, and many other fields. They are used to solve problems involving right triangles and periodic phenomena.

4. Using the Calculator

Tips: You can either:

Enter any two sides to calculate the ratios
Enter the angle to calculate theoretical ratios
Combine angle and side information for more precise calculations

5. Frequently Asked Questions (FAQ)

Q1: What if my triangle isn't right-angled?
A: These ratios only work for right triangles. For other triangles, you'll need the Law of Sines or Cosines.

Q2: Why do I sometimes get errors?
A: Make sure your inputs follow triangle rules (hypotenuse must be longest side, angles between 0-90°).

Q3: Can I calculate angles with this?
A: This calculator focuses on ratios. For angles, you'd need inverse trigonometric functions.

Q4: What units should I use?
A: Units must be consistent (all meters, all cm, etc.). The calculator displays ratios which are unitless.

Q5: How precise are the results?
A: Results are rounded to 4 decimal places. For most practical applications, this is sufficient.