Triangle Calculator Sin Cos Tan

Trigonometric Ratios:

\[ \sin(\theta) = \frac{opp}{hyp} \] \[ \cos(\theta) = \frac{adj}{hyp} \] \[ \tan(\theta) = \frac{opp}{adj} \]

Angle (θ):

degrees

Opposite Side:

units

Adjacent Side:

units

Hypotenuse:

units

Results:

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1. What Are Trigonometric Ratios?

Trigonometric ratios (sine, cosine, tangent) relate the angles of a right triangle to the lengths of its sides. These ratios are fundamental in geometry, physics, engineering, and many other fields.

2. How Does the Calculator Work?

The calculator uses the basic trigonometric formulas:

\[ \sin(\theta) = \frac{opp}{hyp} \] \[ \cos(\theta) = \frac{adj}{hyp} \] \[ \tan(\theta) = \frac{opp}{adj} \]

Where:

\( \theta \) — Angle in degrees
\( opp \) — Length of side opposite to angle θ
\( adj \) — Length of side adjacent to angle θ
\( hyp \) — Length of hypotenuse

Explanation: The calculator can compute trigonometric ratios from the angle, or calculate missing sides when given the angle and at least one side length.

3. Importance of Trigonometry

Details: Trigonometric functions are essential for solving problems involving right triangles, periodic phenomena, waves, circular motion, and many real-world applications in science and engineering.

4. Using the Calculator

Tips: Enter the angle in degrees and at least one side length. The calculator will compute all trigonometric ratios and any missing side lengths that can be determined from the given information.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between degrees and radians?
A: Degrees (0-360) and radians (0-2π) are different angle measures. This calculator uses degrees by default.

Q2: What if my triangle isn't right-angled?
A: These formulas only work for right triangles. For other triangles, you'd need the Law of Sines or Cosines.

Q3: Why do I sometimes get "undefined" for tangent?
A: Tangent is undefined at 90° because it would require division by zero (adjacent side = 0).

Q4: Can I use this for navigation problems?
A: Yes, trigonometric ratios are commonly used in navigation, surveying, and GPS calculations.

Q5: How accurate are the calculations?
A: The calculator provides results with 4 decimal places for ratios and 2 decimal places for side lengths.