Sin Cos Tan Calculator

Trigonometric Functions:

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

Sine (sin):

Cosine (cos):

Tangent (tan):

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1. What Are Trigonometric Functions?

Trigonometric functions (sine, cosine, and tangent) relate angles of a right triangle to ratios of its sides. These functions are fundamental in mathematics, physics, engineering, and many other fields.

2. How Does the Calculator Work?

The calculator uses PHP's built-in 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 radians or degrees
opposite — Side opposite to angle θ
adjacent — Side adjacent to angle θ
hypotenuse — Longest side of the right triangle

Note: PHP's trigonometric functions expect angles in radians. If degrees are selected, the calculator converts them to radians first.

3. Applications of Trigonometric Functions

Details: Trigonometric functions are used in navigation, engineering, physics, computer graphics, architecture, and many other fields where angle measurements and periodic phenomena are important.

4. Using the Calculator

Tips: Enter the angle value and select whether it's in degrees or radians. The calculator will compute the sine, cosine, and tangent of the angle.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between degrees and radians?
A: Degrees divide a circle into 360 equal parts, while radians are based on the radius of the circle (2π radians = 360°).

Q2: Why does tan(90°) return a large number instead of infinity?
A: Due to floating-point precision limitations, calculators return very large numbers instead of true infinity for angles approaching 90°.

Q3: What are the ranges of trigonometric function values?
A: Sine and cosine values range between -1 and 1, while tangent can be any real number.

Q4: Can I calculate inverse trigonometric functions with this calculator?
A: No, this calculator only computes the standard trigonometric functions (sin, cos, tan).

Q5: Why are my results slightly different from other calculators?
A: Small differences may occur due to different rounding methods or floating-point precision implementations.