Sexagecimal System /Angles And Measurements/Trigonometry/Applied Maths Ist / New Syllabus #bteup
Education
Introduction
Welcome to Amplitude Studies 2.0! In this article, we are excited to introduce the updated syllabus for Applied Mathematics I for UP Polytechnic, focusing specifically on the first unit: Trigonometry. Although trigonometry has been a part of the syllabus in the past, the new curriculum includes additional content that we will explore in detail.
Understanding Trigonometry
Trigonometry is a branch of mathematics that deals with the relationships between the angles and sides of triangles. For any triangle, there are three sides labeled as A, B, and C and corresponding angles also referred to as A, B, and C. Understanding the relationship between these angles and sides is fundamental in trigonometry.
What is an Angle?
An angle is formed when two lines intersect. The point of intersection is called the vertex, while the two lines are referred to as the sides of the angle. The measurement of angles can be approached in different ways, but we’ll start with some definitions and terminology to build our foundation.
Initial Line and Terminal Line:
- The line from which the angle starts is called the initial line (or zero line).
- When this line is rotated, it creates an angle, which terminates at a second line called the terminal line.
Positive and Negative Angles
Angles can be categorized as positive or negative based on the direction of rotation:
- Positive Angles: These are formed when the terminal line rotates in an anti-clockwise direction from the initial line.
- Negative Angles: Conversely, a negative angle occurs when the terminal line rotates in a clockwise direction.
To visualize this, think of a clock: the motion of the hands moving clockwise is considered a negative rotation, while moving in the opposite direction (anti-clockwise) is considered a positive rotation.
Measuring Angles
Angle measurement systems have evolved, leading to three primary methods:
Sexagecimal System (Degrees): This British system divides a complete angle (360°) into 360 equal parts, where each part is called one degree. Degrees are further subdivided into minutes (1 degree = 60 minutes) and seconds (1 minute = 60 seconds).
Centigrade or Centisimile System: Developed by the French, this system divides angles into 100 equal parts, rather than degrees.
Radian System: This circular system measures angles in radians, widely used in scientific contexts, particularly in physics.
Central Angle
The central angle is formed when the initial line makes a complete rotation (360°). The complete angle obtained from this rotation is then used as a reference point for further divisions.
Now, let's summarize the content with keywords.
Keyword
- Trigonometry
- Angles
- Sides
- Vertex
- Initial line
- Terminal line
- Positive angle
- Negative angle
- Sexagecimal System
- Degrees
- Centigrade System
- Radian System
- Central angle
- Measurements
FAQ
What is trigonometry? Trigonometry is a mathematical branch concerned with the relationships between the sides and angles of triangles.
How are angles measured in trigonometry? Angles are primarily measured using three systems: Sexagecimal (degrees), Centigrade, and Radian.
What defines a positive angle? A positive angle is created when the terminal line rotates anti-clockwise from the initial line.
What defines a negative angle? A negative angle is formed when the terminal line rotates in a clockwise direction from the initial line.
What is a central angle? The central angle is the angle formed by one complete revolution around the initial line, measured as 360° in the Sexagecimal system.
What are minutes and seconds in angle measurement? A minute in angles is 1/60 of a degree, while a second is 1/60 of a minute. Both are units used to measure very small angles.
Feel free to reach out with any questions or for further clarification on today's topic! Thank you for reading!