Lecture Notes: Trigonometry and Other Mathematical Concepts
1. Introduction
- Angles are unitless and dimensionless.
- Use of angles in circles and right-angle triangles.
2. Types of Angles
- Measurement of Angles in a Circle:
- Through arc length and radius.
- 180 degrees = pi radians.
- Measurement of Angles in a Triangle:
3. Angle Units
- Measurement of angles in degrees and radians.
- Conversion from degrees to radians and radians to degrees.
4. Values of Sine, Cosine, and Tan
- Measurement of values from 0 to 90 degrees and 90 to 180 degrees.
- Calculation of values through mirror images.
5. Rules for Changing Trigonometric Functions
- Negative angles and their values.
- Formula: The interrelationship of sine, cosine, and tan.
6. Phasor Diagram
- 90-degree phase difference between sine and cosine.
- Use of phasor diagram.
7. Graph and Slope
- Straight Line Graph: Measurement of a straight line.
- Parabolic Graph: For y = x^2 and y = -x^2.
8. Logarithm and its Properties
- Basic properties and use of logarithms.
- Conversion from power function to log function.
9. Differentiation and Integration
- Differentiation: Measurement of a function's slope.
- Integration: Measurement of area under the curve.
10. Application
- Use in various chapters of physics:
- Such as wave optics, SHM, thermodynamics, etc.
11. Homework and Practice
- Practice questions based on the given topics.
These notes include all the important mathematical concepts that are useful in physics and other science subjects. This is a precise reference guide for study.