Math Doubts

Sin triple angle formula

Expansion form

$\sin{3\theta} \,=\, 3\sin{\theta}-4\sin^3{\theta}$

Simplified form

$3\sin{\theta}-4\sin^3{\theta} \,=\, \sin{3\theta}$

Introduction

It is called sine triple angle formula and used in two different cases.

  1. Sin of triple angle is expanded as the subtraction of four times sin cubed of angle from three times sin of angle.
  2. The subtraction of four times sin cubed of angle from three times sin of angle is simplified as sin of triple angle.

How to use

Sine triple angle identity is used to either expand or simplify the triple angle trigonometric functions like $\sin{3x}$, $\sin{3A}$, $\sin{3\alpha}$ and etc. For example,

$(1) \,\,\,\,\,\,$ $\sin{3x} \,=\, 3\sin{x}-4\sin^3{x}$

$(2) \,\,\,\,\,\,$ $\sin{3A} \,=\, 3\sin{A}-4\sin^3{A}$

$(3) \,\,\,\,\,\,$ $\sin{3\alpha} \,=\, 3\sin{\alpha}-4\sin^3{\alpha}$

Proof

Learn how to derive the rule of sin triple angle identity by geometrical approach in trigonometry.



Follow us
Email subscription
Math Doubts
Math Doubts is a best place to learn mathematics and from basics to advanced scientific level for students, teachers and researchers. Know more
Follow us on Social Media
Mobile App for Android users Math Doubts Android App
Math Problems

Learn how to solve easy to difficult mathematics problems of all topics in various methods with step by step process and also maths questions for practising.

Learn more