Multiple Angle Formula

What is the multiple angle formula?

Multiple angle formulas in trigonometry is used to find values of trigonometric function when the given angle are in multiple of ‘A’ 2A, 3A, 4A, etc.

How to calculate multiple angles?

To calculate multiple angle follow the formulas added below:

• Half Angle Formulae: sin x = 2 sin(x/2)cos(x/2) = (2 tan (x/2))/(1 + tan²(x/2))
• Double Angle Formulae: sin 2x = 2sin x cos x = (2 tan x)/(1 + tan ²x)
• Triple Angle Formulae: sin 3x = 3sin x – 4sin³x

What is the formula for multiple and sub multiple of an angle?

Formula for multiple and sub multiple of an angle are:

• (sin A/2 + cos A/2)= √(1 + sin A) sin A/2 + cos A/2
• (sin A/2 – cos A/2) = √(1 – sin A)

What are triple angle formulas?

Triple angle formulas in trigonometry are equations that relate the sine, cosine, and tangent of three times an angle to the sine, cosine, and tangent of the original angle, i.e.

• sin(3θ) = 3sin(θ) – 4sin³(θ)
• cos(3θ)=4cos³(θ) – 3cos(θ)
• tan(3θ) = (3tan(θ) – tan³(θ)) / (1 – 3tan²(θ))

Trigonometry is one of the important topics in mathematics that is used in various fields. The trigonometric formulae are applied and used in various formulae, derivations, etc. This article is about the multiple angle formulae in trigonometry where we find sine, cosine, and tangent for multiple angles. This formula can easily evaluate the multiple angles for any given problem. The trigonometric functions with multiple angles are called the multiple-angle formulas. Double, half and triple angles are present under multiple angles.