Six Trigonometric Ratios Calculator

Trigonometric Ratios:

\[ \sin\theta = \frac{opposite}{hypotenuse} \] \[ \cos\theta = \frac{adjacent}{hypotenuse} \] \[ \tan\theta = \frac{opposite}{adjacent} \] \[ \csc\theta = \frac{1}{\sin\theta} \] \[ \sec\theta = \frac{1}{\cos\theta} \] \[ \cot\theta = \frac{1}{\tan\theta} \]

Results:

sin θ =

cos θ =

tan θ =

csc θ =

sec θ =

cot θ =

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1. What Are Trigonometric Ratios?

Trigonometric ratios relate the angles of a right triangle to the ratios of its sides. The six fundamental ratios are sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), and cotangent (cot).

2. How Does the Calculator Work?

The calculator computes all six trigonometric functions for a given angle:

Explanation: The calculator first converts the angle from degrees to radians, then uses PHP's built-in trigonometric functions to compute the ratios.

3. Applications of Trigonometric Ratios

Details: Trigonometric ratios are fundamental in geometry, physics, engineering, navigation, and many scientific fields. They're used to solve triangles, model periodic phenomena, and analyze waveforms.

4. Using the Calculator

Tips: Enter any angle between 0° and 360°. The calculator will display all six trigonometric ratios. Results are rounded to 4 decimal places.

5. Frequently Asked Questions (FAQ)

Q1: What does "undefined" mean in the results?
A: Some ratios become undefined at certain angles (e.g., tan 90° is undefined). This occurs when dividing by zero in the ratio calculation.

Q2: Are the results in degrees or radians?
A: Input is in degrees, but calculations are performed using radians internally. Results are dimensionless ratios.

Q3: How accurate are the results?
A: Results are accurate to machine precision, displayed with 4 decimal places for readability.

Q4: Can I calculate inverse trigonometric functions?
A: This calculator computes ratios from angles. For inverse functions (angles from ratios), you would need a different calculator.

Q5: What about angles beyond 360°?
A: Trigonometric functions are periodic, so angles beyond 360° can be reduced by subtracting multiples of 360°.