A basic mathematical relation between any trigonometric functions is called a basic trigonometric identity. A basic trigonometric identity is usually used as a formula in mathematics. Hence, it is also called as a basic trigonometric formula.

There are four types of basic trigonometric identities in trigonometry and they are used as formulas in mathematics. So, everyone who studies the trigonometry newly must firstly learn all of these basic trigonometric identities.

The following trigonometric formulas derived by taking theta ($\theta$) as angle of a right angled triangle.

Trigonometric ratios form six identities in reciprocal form and learn proofs of these reciprocal formulas.

$(1)\,\,\,\,$ $\sin \theta \,=\, \dfrac{1}{\csc \theta}$

$(2)\,\,\,\,$ $\cos \theta \,=\, \dfrac{1}{\sec \theta}$

$(3)\,\,\,\,$ $\tan \theta \,=\, \dfrac{1}{\cot \theta}$

$(4)\,\,\,\,$ $\cot \theta \,=\, \dfrac{1}{\tan \theta}$

$(5)\,\,\,\,$ $\sec \theta \,=\, \dfrac{1}{\cos \theta}$

$(6)\,\,\,\,$ $\csc \theta \,=\, \dfrac{1}{\sin \theta}$

Trigonometric functions form three formulas in product form and learn the proofs of product identities.

$(1)\,\,\,\,$ $\sin \theta \times \csc \theta = 1 $

$(2)\,\,\,\,$ $\cos \theta \times \sec \theta = 1 $

$(3)\,\,\,\,$ $\tan \theta \times \cot \theta = 1 $

The six trigonometric functions involve in two relations in quotient form and learn the proofs of quotient identities.

$(1)\,\,\,\,$ $\dfrac{\sin \theta}{\cos \theta} = \tan \theta$

$(2)\,\,\,\,$ $\dfrac{\cos \theta}{\sin \theta} = \cot \theta$

The six trigonometric functions form three Pythagorean identities on the basis of Pythagoras Theorem.

$(1)\,\,\,\,$ $\sin^2{\theta} \,+\, \cos^2{\theta} \,=\, 1$

$(2)\,\,\,\,$ $\sec^2{\theta} \,-\, \tan^2{\theta} \,=\, 1$

$(3)\,\,\,\,$ $\csc^2{\theta} \,-\, \cot^2{\theta} \,=\, 1$

List of the questions for practice to learn how to use the basic trigonometric identities in problems.

Latest Math Topics

Nov 03, 2022

Jul 24, 2022

Jul 15, 2022

Latest Math Problems

Nov 25, 2022

Nov 02, 2022

Oct 26, 2022

Oct 24, 2022

Sep 30, 2022

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 maths problems in different methods with understandable steps.

Copyright © 2012 - 2022 Math Doubts, All Rights Reserved