1. What is Tangent?

The tangent of an angle in a right triangle is the ratio of the opposite side to the adjacent side. For small angles like 1°, the tangent is approximately equal to the angle itself in radians.

2. How Does the Calculator Work?

The calculator uses the mathematical tangent function:

For 1° specifically:

• 1° in radians: \( \frac{\pi}{180} \approx 0.0174533 \)
• \( \tan(1°) \approx 0.017455 \) (exact)
• Often approximated as 0.0175 for practical calculations

3. Importance of Tangent Calculation

Details: The tangent function is crucial in trigonometry, physics, engineering, and navigation. For small angles, it's particularly important in calculations involving slopes, angles of elevation, and small-angle approximations.

4. Using the Calculator

Tips: Enter any angle between 0° and 90° to calculate its tangent. The default value is 1° which gives approximately 0.0175.

5. Frequently Asked Questions (FAQ)

Q1: Why is tan(1°) approximately 0.0175?
A: Because 1° is about 0.0174533 radians, and for small angles, tan(θ) ≈ θ in radians.

Q2: How accurate is the 0.0175 approximation?
A: It's accurate to 3 decimal places (0.0175 vs exact 0.017455), sufficient for many practical applications.

Q3: Where is tan(1°) commonly used?
A: In surveying, engineering slope calculations, and any field requiring small angle measurements.

Q4: What's the difference between tan(1°) and tan(1)?
A: tan(1) calculates tangent of 1 radian (≈57.3°), while tan(1°) calculates tangent of 1 degree.

Q5: Can I calculate tangent for angles greater than 90°?
A: This calculator is limited to 0-90° for simplicity. Tangent is periodic with period 180°.