
CBSE Important Questions›

CBSE Previous Year Question Papers›
 CBSE Previous Year Question Papers
 CBSE Previous Year Question Papers Class 12
 CBSE Previous Year Question Papers Class 10

CBSE Revision Notes›

CBSE Syllabus›

CBSE Extra Questions›

CBSE Sample Papers›
 CBSE Sample Papers
 CBSE Sample Question Papers For Class 5
 CBSE Sample Question Papers For Class 4
 CBSE Sample Question Papers For Class 3
 CBSE Sample Question Papers For Class 2
 CBSE Sample Question Papers For Class 1
 CBSE Sample Question Papers For Class 12
 CBSE Sample Question Papers For Class 11
 CBSE Sample Question Papers For Class 10
 CBSE Sample Question Papers For Class 9
 CBSE Sample Question Papers For Class 8
 CBSE Sample Question Papers For Class 7
 CBSE Sample Question Papers For Class 6

ISC & ICSE Syllabus›

ICSE Question Paper›
 ICSE Question Paper
 ISC Class 12 Question Paper
 ICSE Class 10 Question Paper

ICSE Sample Question Papers›
 ICSE Sample Question Papers
 ISC Sample Question Papers For Class 12
 ISC Sample Question Papers For Class 11
 ICSE Sample Question Papers For Class 10
 ICSE Sample Question Papers For Class 9
 ICSE Sample Question Papers For Class 8
 ICSE Sample Question Papers For Class 7
 ICSE Sample Question Papers For Class 6

ICSE Revision Notes›
 ICSE Revision Notes
 ICSE Class 9 Revision Notes
 ICSE Class 10 Revision Notes

ICSE Important Questions›

Maharashtra board›

RajasthanBoard›
 RajasthanBoard

Andhrapradesh Board›
 Andhrapradesh Board
 AP Board Sample Question Paper
 AP Board syllabus
 AP Board Previous Year Question Paper

Telangana Board›

Tamilnadu Board›

NCERT Solutions Class 12›
 NCERT Solutions Class 12
 NCERT Solutions Class 12 Economics
 NCERT Solutions Class 12 English
 NCERT Solutions Class 12 Hindi
 NCERT Solutions Class 12 Maths
 NCERT Solutions Class 12 Physics
 NCERT Solutions Class 12 Accountancy
 NCERT Solutions Class 12 Biology
 NCERT Solutions Class 12 Chemistry
 NCERT Solutions Class 12 Commerce

NCERT Solutions Class 10›

NCERT Solutions Class 11›
 NCERT Solutions Class 11
 NCERT Solutions Class 11 Statistics
 NCERT Solutions Class 11 Accountancy
 NCERT Solutions Class 11 Biology
 NCERT Solutions Class 11 Chemistry
 NCERT Solutions Class 11 Commerce
 NCERT Solutions Class 11 English
 NCERT Solutions Class 11 Hindi
 NCERT Solutions Class 11 Maths
 NCERT Solutions Class 11 Physics

NCERT Solutions Class 9›

NCERT Solutions Class 8›

NCERT Solutions Class 7›

NCERT Solutions Class 6›

NCERT Solutions Class 5›
 NCERT Solutions Class 5
 NCERT Solutions Class 5 EVS
 NCERT Solutions Class 5 English
 NCERT Solutions Class 5 Maths

NCERT Solutions Class 4›

NCERT Solutions Class 3›

NCERT Solutions Class 2›
 NCERT Solutions Class 2
 NCERT Solutions Class 2 Hindi
 NCERT Solutions Class 2 Maths
 NCERT Solutions Class 2 English

NCERT Solutions Class 1›
 NCERT Solutions Class 1
 NCERT Solutions Class 1 English
 NCERT Solutions Class 1 Hindi
 NCERT Solutions Class 1 Maths

JEE Main Question Papers›

JEE Main Syllabus›
 JEE Main Syllabus
 JEE Main Chemistry Syllabus
 JEE Main Maths Syllabus
 JEE Main Physics Syllabus

JEE Main Questions›
 JEE Main Questions
 JEE Main Maths Questions
 JEE Main Physics Questions
 JEE Main Chemistry Questions

JEE Main Mock Test›
 JEE Main Mock Test

JEE Main Revision Notes›
 JEE Main Revision Notes

JEE Main Sample Papers›
 JEE Main Sample Papers

JEE Advanced Question Papers›

JEE Advanced Syllabus›
 JEE Advanced Syllabus

JEE Advanced Mock Test›
 JEE Advanced Mock Test

JEE Advanced Questions›
 JEE Advanced Questions
 JEE Advanced Chemistry Questions
 JEE Advanced Maths Questions
 JEE Advanced Physics Questions

JEE Advanced Sample Papers›
 JEE Advanced Sample Papers

NEET Eligibility Criteria›
 NEET Eligibility Criteria

NEET Question Papers›

NEET Sample Papers›
 NEET Sample Papers

NEET Syllabus›

NEET Mock Test›
 NEET Mock Test

NCERT Books Class 9›
 NCERT Books Class 9

NCERT Books Class 8›
 NCERT Books Class 8

NCERT Books Class 7›
 NCERT Books Class 7

NCERT Books Class 6›
 NCERT Books Class 6

NCERT Books Class 5›
 NCERT Books Class 5

NCERT Books Class 4›
 NCERT Books Class 4

NCERT Books Class 3›
 NCERT Books Class 3

NCERT Books Class 2›
 NCERT Books Class 2

NCERT Books Class 1›
 NCERT Books Class 1

NCERT Books Class 12›
 NCERT Books Class 12

NCERT Books Class 11›
 NCERT Books Class 11

NCERT Books Class 10›
 NCERT Books Class 10

Chemistry Full Forms›
 Chemistry Full Forms

Biology Full Forms›
 Biology Full Forms

Physics Full Forms›
 Physics Full Forms

Educational Full Form›
 Educational Full Form

Examination Full Forms›
 Examination Full Forms

Algebra Formulas›
 Algebra Formulas

Chemistry Formulas›
 Chemistry Formulas

Geometry Formulas›
 Geometry Formulas

Math Formulas›
 Math Formulas

Physics Formulas›
 Physics Formulas

Trigonometry Formulas›
 Trigonometry Formulas

CUET Admit Card›
 CUET Admit Card

CUET Application Form›
 CUET Application Form

CUET Counselling›
 CUET Counselling

CUET Cutoff›
 CUET Cutoff

CUET Previous Year Question Papers›
 CUET Previous Year Question Papers

CUET Results›
 CUET Results

CUET Sample Papers›
 CUET Sample Papers

CUET Syllabus›
 CUET Syllabus

CUET Eligibility Criteria›
 CUET Eligibility Criteria

CUET Exam Centers›
 CUET Exam Centers

CUET Exam Dates›
 CUET Exam Dates

CUET Exam Pattern›
 CUET Exam Pattern
Angle Formula – When two lines or planes cross, the degree of rotation around that point that is necessary to align one with the other is called an angle. In geometric forms, it is a critical measurement. An angle is formed when two intersecting rays, known as the angle’s arms, meet at a common point. The vertex of an angle is the point where its corner points meet. Angle formulae are used to compute angle measurements. Angle formulae exist in a number of formats. Some examples are the doubleangle formula, halfangle formula, compound angle formula, internal angle formula, and others. This post examine at the angle formula, its different types, and some relevant sample problems.
Quick Links
ToggleAngle Formula
The angle is a shape formed by two lines or rays diverging from the vertex, the common point. When two rays or halflines projected with the same termination cross each other, an angle is formed. The angle’s vertex represents the corner points, while the rays represent the sides, or the arms. Angles are measured in degrees or radians.
Angles are measured in degrees or radians. A radian is the angle generated by enclosing the radius of a circle around its circumference to create an arc in a circle. The angle between two lines can be expressed using both radians and degrees. The whole angle of a circle is 360 degrees, often known as two radians. Using a formula, angles may be transformed from radians to degrees. As a result, the degree (°), radians, or gradians are frequently employed to describe angles.
What Are Angle Formulas?
The measurements of the angles are determined using the Angle Formula. Two rays that cross at the same point and are referred to as the angel’s arms are what make up an angle. The vertex of the angle is the name for the angle’s corner point. The amount of rotation between the two lines is referred to as the angle. Angles are expressed in radians or degrees.
The formulae for the angle created at the circle’s centre by two radii and an arc have been covered in this article. Let’s also concentrate on the trigonometric formulae for numerous angles and double angles. The Extramarkrs provide all the important information about the Angle Formula.
Different types of Angles
Angles in geometry can be of many different shapes and sizes depending on how they are measured. They serve as the building blocks for more complex geometrical figures and shapes.
Acute angle: An acute angle is any angle that is between 0 and 90 degrees, or higher than 0 and less than 90.
Right angle: The angle that is exactly 90 degrees is referred to as a right angle.
Obtuse angle: An obtuse angle is one that is between 90 and 180 degrees, or higher than 90 and less than 180.
Straight Angle: An angle that is exactly 180 degrees in length is referred to as a straight angle.
Reflex angle: A reflex angle is an angle that is between 180 and 360 degrees, or more than 180 and less than 360.
Complete Angle: A complete angle, also known as a full rotation, is an angle that is exactly 360 degrees in length.
Multiple Angle Formulas
Trigonometric functions frequently contain the many angles. Although it is impossible to directly obtain the values of many angles, their values can be computed by expanding each trigonometric function. The Eulers formula and Binomial Theorem are used to determine these numerous angles of the forms sin nx, cos nx, and tan nx, which are stated in terms of sin x, cos x, and simplify cos x.
List of Multiple Angle Formula
Half Angle Formula
sin x = 2 sin(x/2)cos(x/2) = (2 tan (x/2))/(1 + tan2(x/2))
cos x = cos2(x/2) – sin2(x/2) = 2cos2(x/2) – 1 = 1 – 2sin2(x/2) = (1 – tan2(x/2))/(1 + tan2(x/2))
tan x = (2 tan(x/2))/(1 – tan2(x/2))
sin(x/2) = √((1 – cos x)/2)
cos(x/2) = √((1 + cos x)/2)
tan(x/2) = √((1 – cos x)/(1 + cos x))
Double Angle Formula:
sin 2x = 2sin x cos x = (2 tan x)/(1 + tan 2x)
cos 2x = cos 2x – sin 2x = 2cos 2x – 1 = 1 – 2sin 2x = (1 – tan 2x)/(1 + tan 2x)
tan 2x = (2 tan x)/(1 – tan 2x)
Triple Angle Formula:
sin 3x = 3sin x – 4sin3x
cos 3x = 4cos3x – 3cos x
tan 3x = (3tan x – tan3x)/(1 – 3tan2x)
Double Angle Formulas
Triangle connections involving angles, lengths, and heights are the subject of trigonometry. It provides a number of useful identities that can be used to comprehend and deduce the numerous scientific equations and formulas.This article examines a few particular varieties of trigonometric equations known as the “double Angle Formula.” They get this name because they employ double angle trigonometric functions.
Trigonometric ratios of double angles (2θ) are expressed in terms of trigonometric ratios of single angles (θ) using double Angle Formula. The Pythagorean identities are used to create certain alternative formulae, while the double Angle Formula are special instances of (and are thus derived from) the sum formulas of trigonometry. In each of the aforementioned sum formulas, we may get the double Angle Formula of sin, cos, and tan by changing A = B. We also arrive at a few other formulae by applying the Pythagorean identities.
the double Angle Formula of sin, cos, and tan are,
sin 2A = 2 sin A cos A (or) (2 tan A) / (1 + tan2A)
cos 2A = cos2A – sin2A (or) 2cos2A – 1 (or) 1 – 2sin2A (or) (1 – tan2A) / (1 + tan2A)
tan 2A = (2 tan A) / (1 – tan2A)
What is Central Angle of Circle Formula?
The central angle of a circle formula is used to calculate the angle between two circle radii.Another way to describe a central angle is as an angle that is subtended by the circle’s arc and its two centre radii. The radius vectors make up the arms of the central angle. To compute the central angle, we need the radius of the circle and the measurement of the length of the arc that subtends the central angle at the centre.
Central angle (θ) = (Arc length × 360º)/(2πr) degrees
Where, r is the radius of the circle.
Angle Formula Solved Examples
Example 1: Jill has a circular section with a radius of 9 units and an arc length of 7 units. Using the angles formulae, determine the segment’s angle.
Solution: Arc length = 7π (given)
Radius = 9 units(given)
Using Angles Formulas,
Angle = (Arc Length × 360o)/2π r
Angle = (7π × 360o)/2π × 9}
= 140o degrees.
Therefore, the angle of the segment is 140o
FAQs (Frequently Asked Questions)
1. What does Angle Formula Mean?
The measurements of the angles are determined using the Angle Formula. A figure called an angle is made up of two crossing rays that share a terminal. These rays are referred to as the angle’s arms. The vertex of the angle is the name for the angle’s corner point. The amount of rotation between the two lines is referred to as the angle. The Angle Formula covers a variety of issues, including the central angle of a circle and multiple angles.
2. What is the Angle Formula for a Double Angle?
cos(2a) = cos2(a)–sin2(a) = 2cos2(a) −1 = 1 − 2sin2(a)
sin(2a) = 2sin(a) cos(a)
tan(2a) = 2tan(a) ÷ 1−tan2(a)
3. Using the Angles Formula, Find the Length of the Arc with r = 16 units and the angle is π/2.
The angle made by the arc = 90
The radius of a circle = 16 units
Using Angles Formula, θ = s/r
s = 16π/2
= 8π
Therefore, the length of the arc of a circle is 8π.