Triple Angle Formulas in Trigonometry
In trigonometry, there are six trigonometric functions, hence accordingly there are three six triple angle formulas
- Sine Triple Angle Formula (Sin 3a)
- Cosine Triple Angle Formula (Cos 3a)
- Tangent Triple Angle Formula (Tan 3a)
- Cosecant Triple Angle Formula (Cosec 3a)
- Secant Triple Angle Formula (Sec 3a)
- Cotangent Triple Angle Formula (Cot 3a)
Sin 3a Formula
Sin 3a Formula is given as
sin(3a) = 3sin(a) – 4sin3(a)
Cos 3a Formula
Cos 3a formula is given as
cos(3a) = 4cos3(a) – 3cos(a)
Tan 3a Formula
Tan 3a formula is given as
tan(3a) = (3tan(a) – tan3(a)) / (1 – 3tan2(a))
Cosec 3a Formula
Cosec 3a formula is given as
cosec(3a) = 1 / (3sin(a) – 4sin3(a))
Sec 3a Formula
Sec 3a formula is given as
sec(3a) = 1 / (4cos3(a) – 3cos(a))
Cot 3a Formula
Cot 3a formula is given as
cot(3a) = (1 – 3tan2(a)) / (3tan(a) – tan3(a))
Triple Angle Formulas
Triple Angle Formulas or Triple Angle Identities are an extension of the Double Angle Formulas in trigonometry. They express trigonometric functions of three times an angle in terms of functions of the original angle. Understanding these formulas is essential in solving complex trigonometric equations, simplifying expressions, and analyzing various mathematical and real-world problems.
Table of Content
- What are Triple Angle Formulas?
- Triple Angle Formulas in Trigonometry
- Sin 3a Formula
- Cos 3a Formula
- Tan 3a Formula
- Cosec 3a Formula
- Sec 3a Formula
- Cot 3a Formula
- Triple Angle Formula Proof
- Sin(3θ) Proof
- Cos(3θ) Proof
- Tan(3θ) Proof
- Cosec(3θ) Proof
- Sec(3θ) Proof
- Cot(3θ) Proof
- Triple Angle Identities
- Triple Angle Formula Conclusion
- Triple Angle Formula Solved Examples
- Triple Angle Formula Practice question
In this article, we will learn the Triple Angle Formulas for sine, cosine, tangent, cosecant, secant, and cotangent, their derivations, and applications.