Right Triangle Trigonometry Calculator Sin Cos Tan

Right Triangle Trigonometry 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:

units

Adjacent Side:

units

Hypotenuse:

units

sin(θ):

cos(θ):

tan(θ):

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1. What is Right Triangle Trigonometry?

Right triangle trigonometry deals with the relationships between the angles and sides of right triangles. The primary trigonometric functions are sine (sin), cosine (cos), and tangent (tan), which relate specific ratios of sides to angles in right triangles.

2. How Does the Calculator Work?

The calculator uses the fundamental trigonometric ratios:

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

Where:

\( \theta \) — Angle in degrees
opposite — Side opposite to the angle θ
adjacent — Side adjacent to the angle θ
hypotenuse — Longest side (opposite the right angle)

Explanation: The calculator computes the trigonometric functions based on the given angle and any two sides of the right triangle.

3. Importance of Trigonometry Calculations

Details: These calculations are fundamental in geometry, physics, engineering, and many practical applications like construction, navigation, and computer graphics.

4. Using the Calculator

Tips: Enter the angle in degrees and at least two sides of the right triangle. The angle must be between 0 and 90 degrees (non-inclusive).

5. Frequently Asked Questions (FAQ)

Q1: What if I only know one side and the angle?
A: You need at least two sides or one side and another angle to calculate the trigonometric functions meaningfully.

Q2: Can I use radians instead of degrees?
A: This calculator currently uses degrees. Convert radians to degrees by multiplying by (180/π) if needed.

Q3: What's the range of valid angles?
A: For right triangles, angles must be between 0 and 90 degrees (non-inclusive).

Q4: Why do I sometimes get errors?
A: Make sure your inputs form a valid right triangle (Pythagorean theorem must hold: a² + b² = c²).

Q5: How precise are the results?
A: Results are rounded to 4 decimal places for readability while maintaining practical accuracy.