In some cases, it is essential to express trigonometric functions in terms of sum multiple angle trigonometric functions to find their values mathematically. So, learn how to expand trigonometric functions in terms of trigonometric functions which contain sub multiple angles. The following submultiple angle identities are used as formulae in trigonometric mathematics but they are similar to multiple angle formulas.
Learn how to expand trigonometric functions in terms of half angle trigonometric functions.
$(1)\,\,\,\,$ $\sin{\theta}$ $\,=\,$ $2\sin{\Big(\dfrac{\theta}{2}\Big)}\cos{\Big(\dfrac{\theta}{2}\Big)}$
$(2)\,\,\,\,$ $\cos{\theta}$ $\,=\,$ $\cos^2{\Big(\dfrac{\theta}{2}\Big)}-\sin^2{\Big(\dfrac{\theta}{2}\Big)}$
$(3)\,\,\,\,$ $\tan{\theta}$ $\,=\,$ $\dfrac{2\tan{\Big(\dfrac{\theta}{2}\Big)}}{1-\tan^2{\Big(\dfrac{\theta}{2}\Big)}}$
$(4)\,\,\,\,$ $\cot{\theta}$ $\,=\,$ $\dfrac{\cot^2{\Big(\dfrac{\theta}{2}\Big)}-1}{2\cot{\Big(\dfrac{\theta}{2}\Big)}}$
Learn how to expand trigonometric functions in terms of one third angle trigonometric functions.
$(1)\,\,\,\,$ $\sin{\theta}$ $\,=\,$ $3\sin{\Big(\dfrac{\theta}{3}\Big)}-4\sin^3{\Big(\dfrac{\theta}{3}\Big)}$
$(2)\,\,\,\,$ $\cos{\theta}$ $\,=\,$ $4\cos^3{\Big(\dfrac{\theta}{3}\Big)}-3\cos{\Big(\dfrac{\theta}{3}\Big)}$
$(3)\,\,\,\,$ $\tan{\theta}$ $\,=\,$ $\dfrac{3\tan{\Big(\dfrac{\theta}{3}\Big)}-\tan^3{\Big(\dfrac{\theta}{3}\Big)}}{1-3\tan^2{\Big(\dfrac{\theta}{3}\Big)}}$
$(4)\,\,\,\,$ $\cot{\theta}$ $\,=\,$ $\dfrac{3\cot{\Big(\dfrac{\theta}{3}\Big)}-\cot^3{\Big(\dfrac{\theta}{3}\Big)}}{1-3\cot^2{\Big(\dfrac{\theta}{3}\Big)}}$
A best free mathematics education website for students, teachers and researchers.
Learn each topic of the mathematics easily with understandable proofs and visual animation graphics.
Learn how to solve the math problems in different methods with understandable steps and worksheets on every concept for your practice.
Copyright © 2012 - 2022 Math Doubts, All Rights Reserved