trig.png

The image is a set of handwritten notes related to angles and trigonometry. Here’s a breakdown:

1. **Definitions and Concepts:**
   - An angle is defined as a measure of rotation of a given ray about its initial point.
   - The original ray is called the initial side, and after rotation, it's called the terminal side.
   - Positive angles are counterclockwise rotations, while negative angles are clockwise.
   - Notation: 1 degree = 60 minutes, 1 minute = 60 seconds.
   - The angle \( \theta = \frac{l}{r} \), where \( l \) is the arc length and \( r \) is the radius.

2. **Conversion Between Degrees and Radians:**
   - \( 2\pi \) radian = 360°, \( \pi \) radian = 180°, 1 radian = \( \frac{180}{\pi} \) degrees, 1° = \( \frac{\pi}{180} \) radians.
   - Formulas are given for converting between radian and degree measures.

3. **Trigonometric Identities:**
   - Addition and subtraction formulas for sine and cosine.
   - Basic trigonometric identities such as \( \sin^2x + \cos^2x = 1 \), \( 1 + \tan^2x = \sec^2x \), and \( 1 + \cot^2x = \csc^2x \).

4. **Specific Angle Identities:**
   - Identities involving angle transformations, such as \(\cos\left(\frac{\pi}{2} - x\right) = \sin x\), \(\sin\left(\frac{\pi}{2} - x\right) = \cos x\), etc.

5. **Diagrams:**
   - Two illustrations showing rays with marked initial and terminal sides and the direction of rotation.

Highlighting is used to emphasize key concepts and formulas. Different colors are used for distinctions such as positive/negative angles, definitions, and identities.