Double Angle Formulas
Double Angle Formulas
Mathematics, also known as the science of structural relationship and order, is a rational discipline that evolved from the primitive practices of counting, measuring, and describing object shapes. Logical reasoning and quantitative calculation are also covered. As a result, the term “Mathematics” now refers to the study of Mathematics. Mathematical theories assist students in understanding and solving a wide variety of problems in both academic and practical contexts. Solving mathematical puzzles is probably the best brain exercise.
The subject matter of Mathematics has become increasingly organised and sequenced as it has evolved. Mathematicians from many civilizations around the world have studied the subject for centuries. Archimedes (287-212 BC) is regarded as a founding figure in the history of Mathematics. He developed formulas for calculating solid volume and surface area. The Father of Indian Mathematics is Aryabhatt, who was born in 476 CE.
Since the 17th century, Mathematics has been an essential component of Physical Sciences and Technology. Recently, it has been predicted that Mathematics will play a similar role in the quantitative aspects of Life Sciences.
What Are Double Angle Formulas?
The Double Angle Formulas are used to express trigonometric ratios of double angles (2) in terms of single-angle trigonometric ratios (). The Double Angle Formulas are special cases of (and thus derived from) the trigonometric sum formulas, and some alternative formulas are derived by using the Pythagorean identities.
The sum formulas of trigonometry are expressed as:
- sin (A + B) = sin A cos B + cos A sin B
- cos (A + B) = cos A cos B – sin A sin B
- tan (A + B) = (tan A + tan B) / (1 – tan A tan B)
The sin, cos, and tan Double Angle Formulas can be derived by substituting A = B in each of the above sum formulas. one can also derive some alternative formulas using the Pythagorean identities.
Double Angle Formulas
The Double Angle Formulas 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)
Double Angle Formulas Derivation
The Double Angle Formulas derivation is very important for students to learn. Having a thorough understanding of derivations helps students understand the concepts of the chapter well.
Double Angle Formulas of Sin
Students can find the Double Angle Formulas for Sin from the website and mobile application of Extramarks. Extramarks’ study resources explain each and every step in a detailed manner. Students can trust the resources provided by Extramarks as they are written by expert subject teachers.
Double Angle Formulas of Cos
Similarly, students can access the Double Angle Formulas of Cos on the website and mobile application of Extramarks. Extramarks provides the best resources for students’ exam preparation. With the help of Extramarks’ resources, students can prepare effectively for their exams. They can download the resources provided by Extramarks in PDF format.
Double Angle Formulas of Tan
The Double Angle Formulas of Tan are also provided by Extramarks. Extramarks’ resources are the most trustworthy and help students gain confidence while preparing for their exams. They can download all the resources provided from the website and mobile application of Extramarks.
Half Angle Formulas
In trigonometry, the half-angle formula is used to calculate the exact values of trigonometric ratios of angles such as 15° (half of the standard angle 30°), 22.5° (half of the standard angle 45°), and so on. Sine, cosine, tangent, cosecant, secant, and cotangent are trigonometric functions. Students will use the trigonometry table to determine the values for standard angles such as 0°, 30°, 45°, 60°, and 90° for these functions. However, if students need to know the trigonometric values for angles such as 15°, 22.5°, and so on, the half-angle formula comes in handy.
Examples Using Double Angle Formulas
With the help of solved examples, students can learn any topic well. They should therefore refer to solved questions of Double Angle Formulas to understand this topic well. Extramarks provides NCERT solutions to help students solve questions. Students can refer to the NCERT solutions for this topic to refer to solved examples.
FAQs (Frequently Asked Questions)
1. What are Double Angle Formulas?
Double Angle Formulas are used to express trigonometric ratios of double angles (2) in terms of single-angle trigonometric ratios (). The Double Angle Formulas are special cases of (and thus derived from) the trigonometric sum formulas, and some alternative formulas are derived by using the Pythagorean identities.
2. What are the various applications of Double Angle Formulas?
The Double Angle Formulas are used to find the values of trigonometric functions’ double angles using their single angle values. The value of cos 30o, for example, can be used to calculate the value of cos 60o. The double-angle formulas can also be used to calculate the triple-angle formulas.
3. From where can students download other resources related to Double Angle Formulas?
Students can download all resources provided by Extramarks from their website and mobile application.