Class 10 Maths Introduction to Trigonometry Handwritten Notes by Toppers – Download PDF

Are you a Class 10 student looking for comprehensive handwritten notes on coordinate geometry? Look no further! In this article, we will provide you with detailed and valuable handwritten notes prepared by top-performing students. These notes will help you understand the fundamental concepts of coordinate geometry and excel in your mathematics exams. So, let’s dive in and explore this essential topic!

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Class 10 Maths Introduction to Trigonometry – Get here the Handwritten Notes for Class 10 Introduction to Trigonometry. Candidates who are ambitious to qualify the Class 10 with a good score can check this article for Notes. Below we provided the link to access the Notes of Class 10 Maths for the topic Introduction to Trigonometry. You can practice the questions and check your answers from the solutions given after the question. By practicing these resources candidates definitely get the idea of which his/her weak areas and how to prepare well for the examination.

• Class: 10th
• Subject: Math
• Topic: Introduction to Trigonometry
• Resource: Handwritten Notes

Maths Handwritten Notes is based on the new(reduced) syllabus by CBSE.

CBSE Class 10 Maths Introduction to Trigonometry Handwritten Notes

Particularly when it comes to the subject of Mathematics, students desire to have an answer key to help them in evaluating their learning and development. Refer to these solutions when practising and solving the Mathematics exercises from NCERT Textbooks.

1. Introduction to Coordinate Geometry

Coordinate geometry, also known as analytic geometry, is a branch of mathematics that combines algebraic techniques with the principles of geometry. It provides a powerful tool for studying geometric shapes and their properties using numerical coordinates. By assigning coordinates to points on a plane, we can analyze their positions, distances, slopes, and more.

2. Cartesian Coordinate System

The Cartesian coordinate system is the foundation of coordinate geometry. It consists of two perpendicular number lines called the x-axis and the y-axis. The point where these axes intersect is called the origin and is denoted as (0, 0). Any point in the plane can be represented by an ordered pair (x, y), where x is the horizontal distance from the y-axis (positive to the right and negative to the left) and y is the vertical distance from the x-axis (positive upward and negative downward).

3. Plotting Points in a Coordinate Plane

To plot a point on a coordinate plane, we locate its coordinates (x, y) and mark it at the corresponding position. The x-coordinate determines the horizontal position, while the y-coordinate determines the vertical position. By plotting multiple points, we can visualize shapes and patterns on the plane.

4. Distance Formula

The distance formula helps us find the distance between two points in a coordinate plane. For two points (x₁, y₁) and (x₂, y₂), the distance between them, denoted as d, is given by:

d = √((x₂ – x₁)² + (y₂ – y₁)²)

5. Midpoint Formula

The midpoint formula allows us to find the coordinates of the midpoint between two points. For two points (x₁, y₁) and (x₂, y₂), the midpoint (xₘ, yₘ) is given by:

xₘ = (x₁ + x₂) / 2 yₘ = (y₁ + y₂) / 2

6. Section Formula

The section formula helps us divide a line segment into a given ratio. For a line segment joining two points A and B with coordinates (x₁, y₁) and (x₂, y₂), the coordinates of a point P dividing the line segment in the ratio m₁:m₂ are given by:

x = (m₁ * x₂ + m₂ * x₁) / (m₁ + m₂) y = (m₁ * y₂ + m₂ * y₁) / (m₁ + m₂)

7. Slope of a Line

The slope of a line measures its steepness or inclination. It is defined as the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line. The slope, denoted as m, can be calculated using the formula:

m = (y₂ – y₁) / (x₂ – x₁)

8. Types of Lines

8.1 Parallel Lines

Parallel lines are lines that never intersect. They have the same slope but different y-intercepts. The equation of a line parallel to another line with slope m and y-intercept c is given by:

y = mx + c₁

8.2 Perpendicular Lines

Perpendicular lines are lines that intersect at a right angle. The product of their slopes is -1. The equation of a line perpendicular to another line with slope m and y-intercept c is given by:

y = -1/mx + c₂

8.3 Intersecting Lines

Intersecting lines are lines that cross each other at some point. Their slopes are different.

9. Equations of Lines

There are various forms of equations used to represent lines based on different information available. Some commonly used forms are:

9.1 Slope-Intercept Form

The slope-intercept form of a line is given by:

y = mx + c

where m is the slope and c is the y-intercept.

9.2 Point-Slope Form

The point-slope form of a line is given by:

y – y₁ = m(x – x₁)

where (x₁, y₁) is a point on the line and m is the slope.

9.3 Two-Point Form

The two-point form of a line is given by:

(y – y₁) / (x – x₁) = (y₂ – y₁) / (x₂ – x₁)

where (x₁, y₁) and (x₂, y₂) are two points on the line.

9.4 Intercept Form

The intercept form of a line is given by:

x / a + y / b = 1

where a and b are the x-intercept and y-intercept, respectively.

9.5 Normal Form

The normal form of a line is given by:

x * cos(θ) + y * sin(θ) = p

where θ is the angle made by the line with the positive x-axis, and p is the perpendicular distance from the origin.

10. Intercepts of a Line

The intercepts of a line are the points where it intersects the x-axis and y-axis. To find the x-intercept, we set y = 0 in the equation of the line and solve for x. Similarly, to find the y-intercept, we set x = 0 and solve for y.

11. Angle Between Two Lines

The angle between two lines can be determined using the slopes of the lines. If the slopes of the lines are m₁ and m₂, the angle θ between them is given by:

θ = arctan(|(m₁ – m₂) / (1 + m₁ * m₂)|)

12. Distance Between Two Lines

The distance between two lines can be calculated as the shortest distance between any two points on the lines. This can be found using the formula:

d = |c₁ – c₂| / √(m₁² + 1)

where c₁ and c₂ are the y-intercepts of the two lines, and m₁ is the slope of one of the lines.

13. Circle and its Equations

A circle is a set of points equidistant from a fixed point called the center. There are different forms of equations used to represent circles:

13.1 Standard Form

The standard form of a circle’s equation is given by:

(x – h)² + (y – k)² = r²

where (h, k) represents the coordinates of the center and r is the radius.

13.2 General Form

The general form of a circle’s equation is given by:

x² + y² + Dx + Ey + F = 0

where D, E, and F are constants.

13.3 Parametric Form

The parametric form of a circle’s equation is given by:

x = h + r * cos(θ) y = k + r * sin(θ)

where (h, k) represents the coordinates of the center, r is the radius, and θ is the angle.

14. Tangent to a Circle

A tangent to a circle is a line that touches the circle at only one point. The tangent line is perpendicular to the radius drawn to the point of contact.

15. Summary and Conclusion

Coordinate geometry is a crucial topic in mathematics, particularly in Class 10. It provides a powerful framework for understanding and analyzing geometric shapes using numerical coordinates. In this article, we have covered various concepts related to coordinate geometry, including the Cartesian coordinate system, plotting points, distance and midpoint formulas, equations of lines, types of lines, intercepts, angles between lines, circles, and tangents. By mastering these concepts and practicing with handwritten notes prepared by toppers, you can enhance your understanding and excel in your Class 10 mathematics exams.

FAQs

Q: Can I rely solely on these handwritten notes for my Class 10 mathematics exam?

A: While these handwritten notes provide valuable insights and explanations, it is recommended to study from multiple sources and practice solving problems to ensure a comprehensive understanding of the subject.

Q: Can these handwritten notes be used for other grade levels as well?

A: While the content primarily focuses on Class 10 mathematics, many concepts covered in coordinate geometry are applicable to higher grade levels as well.

Q: Are there any practice exercises included in the handwritten notes?

A: The handwritten notes provide detailed explanations and examples for each concept. However, for additional practice, it is recommended to solve textbook exercises and refer to supplementary materials.