Mastering Trigonometric Functions

📋 Course Outline

1. Basic Trigonometric Functions
2. Reciprocal Functions
3. Unit Circle
4. Trigonometric Identities
5. Pythagorean Identities
6. Angle Sum and Difference
7. Double and Half Angle
8. Graphing Functions
9. Inverse Functions
10. Applications in Physics

📖 1. Basic Trigonometric Functions

🔑 Key Concepts & Definitions

• Sine (sin): Ratio of the length of the opposite side to the hypotenuse in a right triangle.
  [ \sin(\theta) = \frac{\text{Opposite}}{\text{Hypotenuse}} ]
• Cosine (cos): Ratio of the length of the adjacent side to the hypotenuse.
  [ \cos(\theta) = \frac{\text{Adjacent}}{\text{Hypotenuse}} ]
• Tangent (tan): Ratio of the opposite side to the adjacent side; also ( \frac{\sin(\theta)}{\cos(\theta)} ).
  [ \tan(\theta) = \frac{\text{Opposite}}{\text{Adjacent}} = \frac{\sin(\theta)}{\cos(\theta)} ]
• Reciprocal functions:
  • Cosecant (csc): ( \frac{1}{\sin(\theta)} )
  • Secant (sec): ( \frac{1}{\cos(\theta)} )
  • Cotangent (cot): ( \frac{1}{\tan(\theta)} = \frac{\cos(\theta)}{\sin(\theta)} )