Basic Trig Functions Calculator

Trigonometric Functions:

\[ \sin(\theta), \cos(\theta), \tan(\theta) \]

Result:

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1. What Are Basic Trigonometric Functions?

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

2. How Does the Calculator Work?

The calculator computes the selected trigonometric function for a given angle:

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

Where:

\( \theta \) — Angle in degrees
opposite — Length of side opposite the angle
adjacent — Length of side adjacent to the angle
hypotenuse — Length of the hypotenuse

Explanation: The calculator converts the angle from degrees to radians before computing the function value.

3. Importance of Trigonometric Calculations

Details: Trigonometric functions are essential for solving problems involving triangles, modeling periodic phenomena, signal processing, and in many areas of science and engineering.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between degrees and radians?
A: Degrees and radians are different units for measuring angles. 360° = 2π radians. This calculator uses degrees as input.

Q2: What are the ranges of trigonometric functions?
A: Sine and cosine output values between -1 and 1. Tangent can be any real number but is undefined at 90° and 270°.

Q3: How accurate are the calculations?
A: The calculator uses PHP's built-in trigonometric functions which are highly accurate (typically to about 15 decimal places).

Q4: Can I calculate inverse trigonometric functions?
A: This calculator only computes the basic functions. For inverse functions (arcsin, arccos, arctan), you would need a different calculator.

Q5: Why does tan(90°) give an error?
A: The tangent function approaches infinity at 90° and is mathematically undefined at exactly 90°.