Formulas of Trigonometric Functions

Basic Trigonometric Formulas:

\[ \sin²(θ) + \cos²(θ) = 1 \] \[ \tan(θ) = \frac{\sin(θ)}{\cos(θ)} \]

sin(θ):

cos(θ):

tan(θ):

csc(θ):

sec(θ):

cot(θ):

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1. What are Trigonometric Functions?

Definition: Trigonometric functions relate angles of a triangle to the ratios of its sides in a right-angled triangle.

Purpose: These functions are fundamental in geometry, physics, engineering, and many scientific calculations.

2. Basic Trigonometric Formulas

The fundamental identities:

\[ \sin²(θ) + \cos²(θ) = 1 \] \[ \tan(θ) = \frac{\sin(θ)}{\cos(θ)} \]

Where:

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

3. Reciprocal Trigonometric Functions

Details: Each primary function has a reciprocal:

\( \csc(θ) = \frac{1}{\sin(θ)} \) — Cosecant
\( \sec(θ) = \frac{1}{\cos(θ)} \) — Secant
\( \cot(θ) = \frac{1}{\tan(θ)} \) — Cotangent

4. Using the Calculator

Tips: Enter any angle in degrees to calculate all six trigonometric function values.

5. Frequently Asked Questions (FAQ)

Q1: What's the range of valid angles?
A: Any real number is valid, though values typically range 0°-360°.

Q2: Why do I get very large numbers for some functions?
A: As θ approaches 90° (or 270°), tan(θ) and sec(θ) approach infinity. Similarly for other functions at specific angles.

Q3: What's the difference between degrees and radians?
A: Degrees range 0-360, radians range 0-2π. This calculator uses degrees.

Q4: How are these functions used in real life?
A: They're essential in physics (waves, oscillations), engineering (structural analysis), navigation, and computer graphics.

Q5: What are some other important trig identities?
A: Important ones include angle sum formulas, double angle formulas, and law of sines/cosines.