Trigonometric Ratio Calculator Degrees

Trigonometric Ratios:

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

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 the standard trigonometric functions:

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

Where:

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

Explanation: The calculator converts the angle from degrees to radians and then applies the appropriate trigonometric function.

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 and to model periodic phenomena.

4. Using the Calculator

Tips: Enter an angle between 0 and 360 degrees and select the trigonometric function you want to calculate. The result will be a unitless ratio.

5. Frequently Asked Questions (FAQ)

Q1: Why do we use degrees instead of radians?
A: Degrees are more commonly used in everyday applications and are easier to visualize for most people. However, mathematical functions typically use radians internally.

Q2: What are the ranges of trigonometric ratios?
A: Sine and cosine values range between -1 and 1, while tangent values can be any real number.

Q3: What happens at 90° and 270° for tangent?
A: The tangent function is undefined at 90° and 270° (and their coterminal angles) because these represent vertical lines where the ratio approaches infinity.

Q4: Can I calculate reciprocal functions?
A: This calculator provides the primary functions. Reciprocal functions (cosecant, secant, cotangent) can be calculated as the reciprocals of these results.

Q5: How accurate are the results?
A: Results are accurate to 6 decimal places, which is sufficient for most practical applications.