Find Value Of Trigonometric Ratio Calculator

Trigonometric Ratios:

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

Result:

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1. What Are Trigonometric Ratios?

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

2. How Does the Calculator Work?

The calculator uses PHP's built-in trigonometric functions to calculate:

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

Where:

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

Explanation: The calculator converts the input angle from degrees to radians (since PHP trigonometric functions use radians) and then calculates the requested trigonometric ratio.

3. Applications of Trigonometric Ratios

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

4. Using the Calculator

Tips: Enter the angle in degrees (0-360), select the trigonometric function you want to calculate (sin, cos, or tan), and click Calculate. The result will show the calculated ratio.

5. Frequently Asked Questions (FAQ)

Q1: What is the range of values for trigonometric ratios?
A: Sine and cosine values range between -1 and 1. Tangent values can be any real number, approaching infinity at 90° and 270°.

Q2: Why do we convert degrees to radians?
A: Most programming languages, including PHP, use radians for trigonometric calculations. One full circle (360°) equals 2π radians.

Q3: What are the reciprocal trigonometric functions?
A: The reciprocals are cosecant (csc = 1/sin), secant (sec = 1/cos), and cotangent (cot = 1/tan).

Q4: How accurate are the calculations?
A: The calculator uses PHP's built-in trigonometric functions which provide high precision results (typically to about 15 decimal places).

Q5: Can I calculate trigonometric ratios for angles beyond 360°?
A: Yes, trigonometric functions are periodic, so angles beyond 360° will give the same result as their equivalent within 0-360°.