This video explores the graphs of trigonometric functions—sine, cosine, tangent, cotangent, secant, and cosecant. We provide a simple and clear explanation of their domain, range, and key features like periodicity, symmetry, and asymptotes.

### What You Will Learn:
✅ **Sine and Cosine**: Smooth wave-like graphs, domain, and range
✅ **Tangent and Cotangent**: Vertical asymptotes and periodicity
✅ **Secant and Cosecant**: U-shaped graphs and undefined points
✅ Understanding the properties and behaviour of each function

This is perfect for students of Class 11 and Class 12 and those preparing for JEE, CBSE, and competitive exams.

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Trigonometric functions—sine, cosine, tangent, cotangent, secant, and cosecant—each have unique graphs, domains, and ranges. Here's a concise overview:

**1. Sine Function (sin x):**
- **Graph**: A smooth, continuous wave oscillating between -1 and 1, repeating every 2π radians.
- **Domain**: All real numbers (-∞, ∞).
- **Range**: [-1, 1].

**2. Cosine Function (cos x):**
- **Graph**: Similar to the sine wave but starts at 1 when x = 0, oscillating between -1 and 1 with a period of 2π radians.
- **Domain**: All real numbers (-∞, ∞).
- **Range**: [-1, 1].

**3. Tangent Function (tan x):**
- **Graph**: Features repeating vertical asymptotes (undefined points) at odd multiples of π/2, with a period of π radians.
- **Domain**: All real numbers except x ≠ (π/2) + nπ, where n is an integer.
- **Range**: All real numbers (-∞, ∞).

**4. Cotangent Function (cot x):**
- **Graph**: Similar to the tangent function but shifted; has vertical asymptotes at multiples of π, with a period of π radians.
- **Domain**: All real numbers except x ≠ nπ, where n is an integer.
- **Range**: All real numbers (-∞, ∞).

**5. Secant Function (sec x):**
- **Graph**: Consists of repeating U-shaped curves with vertical asymptotes where the cosine function is zero, period of 2π radians.
- **Domain**: All real numbers except x ≠ (π/2) + nπ, where n is an integer.
- **Range**: (-∞, -1] ∪ [1, ∞).

**6. Cosecant Function (csc x):**
- **Graph**: Similar to the secant function but based on the sine function, with vertical asymptotes where sine is zero, period of 2π radians.
- **Domain**: All real numbers except x ≠ nπ, where n is an integer.
- **Range**: (-∞, -1] ∪ [1, ∞).

Understanding these properties is crucial for analyzing trigonometric functions and their applications in various fields.

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