Trigonometric Functions Calculator

Trigonometric Functions:

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

Angle (θ):

degrees

Opposite Side:

units

Adjacent Side:

units

Hypotenuse:

units

sin(θ):

cos(θ):

tan(θ):

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1. What Are Trigonometric Functions?

Trigonometric functions relate the angles of a right triangle to the ratios of its sides. The three primary functions are sine (sin), cosine (cos), and tangent (tan), which are fundamental in mathematics, physics, engineering, and many other fields.

2. How Does the Calculator Work?

The calculator uses these fundamental trigonometric relationships:

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

Where:

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

Explanation: The calculator can compute the trigonometric functions for any given angle, and if you provide two sides of a right triangle, it can calculate the missing side using the Pythagorean theorem.

3. Applications of Trigonometry

Details: Trigonometric functions are used in navigation, engineering, physics, architecture, computer graphics, and more. They're essential for calculating distances, angles, and modeling periodic phenomena.

4. Using the Calculator

Tips: Enter the angle in degrees and any two sides of a right triangle. The calculator will compute the trigonometric functions and the missing side if enough information is provided.

5. Frequently Asked Questions (FAQ)

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

Q2: Why does tan(90°) show a very large number?
A: The tangent of 90° is mathematically undefined (approaches infinity) because the adjacent side length approaches zero.

Q3: Can I use this for non-right triangles?
A: These formulas are specifically for right triangles. For other triangles, you would need the Law of Sines or Law of Cosines.

Q4: What's the range of possible values for sin and cos?
A: Both sine and cosine always return values between -1 and 1, inclusive. For angles between 0° and 90°, they're always positive.

Q5: How accurate are the calculations?
A: The calculations are accurate to 4 decimal places for the trigonometric functions and 2 decimal places for side lengths.