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    10 Lessons

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Overview

This course Covers Angles and their measurements from the textbook of HSC Science Std 11th. For students, each and every sum is solved and explained. Enjoy learning!!

Topics students will learn in this course are as follows -

1. Length of the arc of a circle

2. Area of the sector

3. Radian Measurement

4. Degree Measurement

5. Radian to degree conversion of angle and vice versa.

Basic Requirement

  • Anyone who wants to learn

  • SSC passed

Skills Covered

  • Degree to radian conversion

  • Length of the arc

  • Area of the sector

Expert Review

As you are studying Angles and Measurements class 11th in this course, here are some highlighted points and terms you need to study.

When you have mastered the concept of points, lines, and planes, you can then think about what happens when two lines or rays meet at a point. This creates an angle between them.

We use angles throughout geometry to analyze shapes like polygons and polyhedrons. We also use angles to describe the behavior of lines, so we should become acquainted with angles, their terms, and how we measure and describe them. In this course, you will better understand angles and measurements. 

Angle measurement Requirements : 

1) Ruler

2) Compass

3) Protractor

4) Divider

5) Set-squares

6) Protractor

Protractors are commonly used to measure angles. For example, circular or semicircular protractors are usually made of transparent plastic, so they can be placed over shapes on a piece of paper and used to measure angles.

When studying angles and Measurements, these are the terms you need to understand:

What is an Angle?

The chapter begins with the basics. An angle is the rotation of a ray from its initial point to its terminal point. Examples include:

1) Initial side: the original ray

2) Terminal side: the final position of the ray after rotation

3) Vertex: point of rotation

4) Positive angle: if the direction of rotation is anticlockwise

5) Negative angle: if the direction of rotation is clockwise

Properties of Angles

Angles are measured in degrees, a measure of circularity or rotation.

One full rotation from centre of a circle is 360°, which would bring you back to your original position. As a result, a half-circle is 180°, and a quarter-circle, or right angle, is 90°.

How do Degrees and Radians differ from each other?

To describe or measure an angle, we usually use 'degrees' as the unit of measurement. You may find that angles are sometimes referred to in radians, however.

The radian is the standard unit of measurement for angles in the Standard International System (SI).

Our previous discussion mentioned that the full rotation of angles through a circular arc is 360°. Therefore, it is also equal to 2π radians, where π (pi) is a special number equaling (approximately) 3.142 (there is more about π on our page on Special Numbers and Concepts).

Radians are represented by 360/2* = 57.3°. Pi is also used to calculate areas and circumferences of circles and to calculate sphere volumes. For more information, review the course and understand it in detail. After completing this course you will be able to solve the maths chapter solution.

Directed Angles: 

Directed angle refers to the pair of ordered rays (OA,OB) as well as the rotation of the ray OA with respect to the position of the ray OB. The measure of directed angle is positive if the rotation of the initial ray is anticlockwise, and negative if it is clockwise. As illustrated by the ordered pair (OA,OB), the ray OA represents the initial arm, and the ray OB represents the terminal arm.

Zero angle:

The angle so formed is zero if the ray OA is no longer rotating, that is it is not rotating. The initial arm is then a terminal arm OB.

A rotation angle is formed when the initial ray OA coincides with the terminal ray OB after one complete rotation.

Straight angle: 

Straight angle is formed when, after a rotation, the rays from the initial angle OA and the terminal angle OB face each other in opposite directions.

Right angle: 

The right angle of one fourth of one rotation angle is also half of a straight angle. Four right angles make up one rotation angle.

Right angle: 

Right angles, which are half of straight angles, make up a fourth of a rotation angle. 4 right angles equals 1 rotation angle

Angle in a Quadrant: 

If the terminal ray of a directed angle lies in a particular quadrant in standard position, then the angle is said to belong to that quadrant Angles

A quadrantal angle is a directed angle whose terminal ray lies along the X-axis or the Y-axis of a standard position.

Co-terminal angles: 

In mathematics, co-terminal angles are directed angles of different amounts of rotation with the same initial and terminal ray positions.

Overview

This course Covers Angles and their measurements from the textbook of HSC Science Std 11th. For students, each and every sum is solved and explained. Enjoy learning!!

Topics students will learn in this course are as follows -

1. Length of the arc of a circle

2. Area of the sector

3. Radian Measurement

4. Degree Measurement

5. Radian to degree conversion of angle and vice versa.

  • Degree to radian conversion

  • Length of the arc

  • Area of the sector

  • Anyone who wants to learn

  • SSC passed

As you are studying Angles and Measurements class 11th in this course, here are some highlighted points and terms you need to study.

When you have mastered the concept of points, lines, and planes, you can then think about what happens when two lines or rays meet at a point. This creates an angle between them.

We use angles throughout geometry to analyze shapes like polygons and polyhedrons. We also use angles to describe the behavior of lines, so we should become acquainted with angles, their terms, and how we measure and describe them. In this course, you will better understand angles and measurements. 

Angle measurement Requirements : 

1) Ruler

2) Compass

3) Protractor

4) Divider

5) Set-squares

6) Protractor

Protractors are commonly used to measure angles. For example, circular or semicircular protractors are usually made of transparent plastic, so they can be placed over shapes on a piece of paper and used to measure angles.

When studying angles and Measurements, these are the terms you need to understand:

What is an Angle?

The chapter begins with the basics. An angle is the rotation of a ray from its initial point to its terminal point. Examples include:

1) Initial side: the original ray

2) Terminal side: the final position of the ray after rotation

3) Vertex: point of rotation

4) Positive angle: if the direction of rotation is anticlockwise

5) Negative angle: if the direction of rotation is clockwise

Properties of Angles

Angles are measured in degrees, a measure of circularity or rotation.

One full rotation from centre of a circle is 360°, which would bring you back to your original position. As a result, a half-circle is 180°, and a quarter-circle, or right angle, is 90°.

How do Degrees and Radians differ from each other?

To describe or measure an angle, we usually use 'degrees' as the unit of measurement. You may find that angles are sometimes referred to in radians, however.

The radian is the standard unit of measurement for angles in the Standard International System (SI).

Our previous discussion mentioned that the full rotation of angles through a circular arc is 360°. Therefore, it is also equal to 2π radians, where π (pi) is a special number equaling (approximately) 3.142 (there is more about π on our page on Special Numbers and Concepts).

Radians are represented by 360/2* = 57.3°. Pi is also used to calculate areas and circumferences of circles and to calculate sphere volumes. For more information, review the course and understand it in detail. After completing this course you will be able to solve the maths chapter solution.

Directed Angles: 

Directed angle refers to the pair of ordered rays (OA,OB) as well as the rotation of the ray OA with respect to the position of the ray OB. The measure of directed angle is positive if the rotation of the initial ray is anticlockwise, and negative if it is clockwise. As illustrated by the ordered pair (OA,OB), the ray OA represents the initial arm, and the ray OB represents the terminal arm.

Zero angle:

The angle so formed is zero if the ray OA is no longer rotating, that is it is not rotating. The initial arm is then a terminal arm OB.

A rotation angle is formed when the initial ray OA coincides with the terminal ray OB after one complete rotation.

Straight angle: 

Straight angle is formed when, after a rotation, the rays from the initial angle OA and the terminal angle OB face each other in opposite directions.

Right angle: 

The right angle of one fourth of one rotation angle is also half of a straight angle. Four right angles make up one rotation angle.

Right angle: 

Right angles, which are half of straight angles, make up a fourth of a rotation angle. 4 right angles equals 1 rotation angle

Angle in a Quadrant: 

If the terminal ray of a directed angle lies in a particular quadrant in standard position, then the angle is said to belong to that quadrant Angles

A quadrantal angle is a directed angle whose terminal ray lies along the X-axis or the Y-axis of a standard position.

Co-terminal angles: 

In mathematics, co-terminal angles are directed angles of different amounts of rotation with the same initial and terminal ray positions.

Course Overview

This course Covers Angles and their measurements from the textbook of HSC Science Std 11th. For students, each and every sum is solved and explained. Enjoy learning!!

Topics students will learn in this course are as follows -

1. Length of the arc of a circle

2. Area of the sector

3. Radian Measurement

4. Degree Measurement

5. Radian to degree conversion of angle and vice versa.

Basic Requirements

  • Anyone who wants to learn

  • SSC passed

Skills Covered

  • Degree to radian conversion

  • Length of the arc

  • Area of the sector

Expert Review

As you are studying Angles and Measurements class 11th in this course, here are some highlighted points and terms you need to study.

When you have mastered the concept of points, lines, and planes, you can then think about what happens when two lines or rays meet at a point. This creates an angle between them.

We use angles throughout geometry to analyze shapes like polygons and polyhedrons. We also use angles to describe the behavior of lines, so we should become acquainted with angles, their terms, and how we measure and describe them. In this course, you will better understand angles and measurements. 

Angle measurement Requirements : 

1) Ruler

2) Compass

3) Protractor

4) Divider

5) Set-squares

6) Protractor

Protractors are commonly used to measure angles. For example, circular or semicircular protractors are usually made of transparent plastic, so they can be placed over shapes on a piece of paper and used to measure angles.

When studying angles and Measurements, these are the terms you need to understand:

What is an Angle?

The chapter begins with the basics. An angle is the rotation of a ray from its initial point to its terminal point. Examples include:

1) Initial side: the original ray

2) Terminal side: the final position of the ray after rotation

3) Vertex: point of rotation

4) Positive angle: if the direction of rotation is anticlockwise

5) Negative angle: if the direction of rotation is clockwise

Properties of Angles

Angles are measured in degrees, a measure of circularity or rotation.

One full rotation from centre of a circle is 360°, which would bring you back to your original position. As a result, a half-circle is 180°, and a quarter-circle, or right angle, is 90°.

How do Degrees and Radians differ from each other?

To describe or measure an angle, we usually use 'degrees' as the unit of measurement. You may find that angles are sometimes referred to in radians, however.

The radian is the standard unit of measurement for angles in the Standard International System (SI).

Our previous discussion mentioned that the full rotation of angles through a circular arc is 360°. Therefore, it is also equal to 2π radians, where π (pi) is a special number equaling (approximately) 3.142 (there is more about π on our page on Special Numbers and Concepts).

Radians are represented by 360/2* = 57.3°. Pi is also used to calculate areas and circumferences of circles and to calculate sphere volumes. For more information, review the course and understand it in detail. After completing this course you will be able to solve the maths chapter solution.

Directed Angles: 

Directed angle refers to the pair of ordered rays (OA,OB) as well as the rotation of the ray OA with respect to the position of the ray OB. The measure of directed angle is positive if the rotation of the initial ray is anticlockwise, and negative if it is clockwise. As illustrated by the ordered pair (OA,OB), the ray OA represents the initial arm, and the ray OB represents the terminal arm.

Zero angle:

The angle so formed is zero if the ray OA is no longer rotating, that is it is not rotating. The initial arm is then a terminal arm OB.

A rotation angle is formed when the initial ray OA coincides with the terminal ray OB after one complete rotation.

Straight angle: 

Straight angle is formed when, after a rotation, the rays from the initial angle OA and the terminal angle OB face each other in opposite directions.

Right angle: 

The right angle of one fourth of one rotation angle is also half of a straight angle. Four right angles make up one rotation angle.

Right angle: 

Right angles, which are half of straight angles, make up a fourth of a rotation angle. 4 right angles equals 1 rotation angle

Angle in a Quadrant: 

If the terminal ray of a directed angle lies in a particular quadrant in standard position, then the angle is said to belong to that quadrant Angles

A quadrantal angle is a directed angle whose terminal ray lies along the X-axis or the Y-axis of a standard position.

Co-terminal angles: 

In mathematics, co-terminal angles are directed angles of different amounts of rotation with the same initial and terminal ray positions.

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Course creator


                                 Amit Patil

Amit Patil

B.E Mechanical Engineering from Mumbai University. 6 years of teaching experience for JEE, BITSAT, VITEEE, etc