Find The Trigonometric Ratio Calculator

Trigonometric Ratios:

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

Trigonometric Ratio:

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1. What Are Trigonometric Ratios?

Trigonometric ratios (sine, cosine, and tangent) are fundamental mathematical functions that relate the angles of a right triangle to the ratios of its sides. They are essential tools in geometry, physics, engineering, and many other fields.

2. How Does the Calculator Work?

The calculator uses standard trigonometric functions:

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

Where:

\( \theta \) — Angle in degrees
\( \sin \) — Sine function
\( \cos \) — Cosine function
\( \tan \) — Tangent function

Explanation: The calculator converts the input angle from degrees to radians and then applies the selected trigonometric function to calculate the ratio.

3. Importance of Trigonometric Ratios

Details: Trigonometric ratios are crucial for solving problems involving right triangles, analyzing periodic phenomena, signal processing, navigation, and many scientific applications. They form the foundation of trigonometry and are used extensively in higher mathematics.

4. Using the Calculator

Tips: Enter an angle between 0 and 360 degrees, select the trigonometric function you want to calculate (sine, cosine, or tangent), and click calculate. The result will show the calculated ratio.

5. Frequently Asked Questions (FAQ)

Q1: What is the range of valid angle inputs?
A: The calculator accepts angles from 0 to 360 degrees. Angles outside this range can be normalized using periodicity properties of trigonometric functions.

Q2: Why are the results sometimes negative?
A: Trigonometric functions can return negative values depending on the quadrant of the angle. For example, cosine is negative in the second and third quadrants.

Q3: What about undefined values for tangent?
A: Tangent is undefined at 90° and 270° (and their coterminal angles) because these angles result in division by zero (cosine = 0).

Q4: Can I calculate inverse trigonometric functions?
A: This calculator calculates standard trigonometric functions. For inverse functions (arcsine, arccosine, arctangent), you would need a different calculator.

Q5: How accurate are the results?
A: The results are calculated using PHP's built-in trigonometric functions, which provide high precision (typically double-precision floating point).