math formulas

# List of Trigonometry Formulas PDF

Trigonometry formulas are a set of different formulas containing trigonometric identities used to solve problems based on the sides and angles of a right-angled triangle. In our article, we will list the trigonometry formulas. We will see trigonometric identities. You will also be able to download these formulas in PDF form.

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## Basic Trigonometry Formulas

#### Trigonometric Ratio Formulas

• sin Î¸ = Perpendicular/Hypotenuse
• cos Î¸ = Base/Hypotenuse
• tan Î¸ = Perpendicular/Base
• sec Î¸ = Hypotenuse/Base
• cosec Î¸ = Hypotenuse/Perpendicular
• cot Î¸ = Base/Perpendicular

### Trigonometry Formulas Involving Reciprocal Identities

• cosec Î¸ = 1/sin Î¸
• sec Î¸ = 1/cos Î¸
• cot Î¸ = 1/tan Î¸
• sin Î¸ = 1/cosec Î¸
• cos Î¸ = 1/sec Î¸
• tan Î¸ = 1/cot Î¸

### Sine Area Formula

(sin A)/a = (sin B)/b = (sin C)/c

### The Law of Cosines

• a2Â = b2Â + c2Â – 2bc cosA
• b2Â = a2Â + c2Â – 2ac cosB
• c2Â = a2Â + b2Â  2ab cosC

### Trigonometry Formulas Involving Half-Angle Identities

sin (x/2) = Â±âˆš[(1 – cos x)/2]

cos (x/2) = Â± âˆš[(1 + cos x)/2]

tan (x/2) = Â±âˆš[(1 – cos x)/(1 + cos x)]

or, tan (x/2) = Â±âˆš[(1 – cos x)(1 – cos x)/(1 + cos x)(1 – cos x)]

tan (x/2) = Â±âˆš[(1 – cos x)2/(1 – cos2x)]

â‡’ tan (x/2) = (1 – cos x)/sin x

### Trigonometry Formulas Involving Periodic Identities(in Radians)

• sin (Ï€/2 â€“ Î¸) = cos Î¸
• cos (Ï€/2 â€“ Î¸) = sin Î¸
• sin (Ï€/2 + Î¸) = cos Î¸
• cos (Ï€/2 + Î¸) = â€“ sin Î¸

• sin (3Ï€/2 â€“ Î¸) = â€“ cos Î¸
• cos (3Ï€/2 â€“ Î¸) = â€“ sin Î¸
• sin (3Ï€/2 + Î¸) = â€“ cos Î¸
• cos (3Ï€/2 + Î¸) = sin Î¸

• sin (Ï€ â€“ Î¸) = sin Î¸
• cos (Ï€ â€“ Î¸) = â€“ cos Î¸
• sin (Ï€ + Î¸) = â€“ sin Î¸
• cos (Ï€ + Î¸) = â€“ cos Î¸

• sin (2Ï€ â€“ Î¸) = â€“ sin Î¸
• cos (2Ï€ â€“ Î¸) = cos Î¸
• sin (2Ï€ + Î¸) = sin Î¸
• cos (2Ï€ + Î¸) = cos Î¸

### Trigonometry Formulas Involving Co-function Identities(in Degrees)

• sin(90Â° âˆ’ x) = cos x
• cos(90Â° âˆ’ x) = sin x
• tan(90Â° âˆ’ x) = cot x
• cot(90Â° âˆ’ x) = tan x
• sec(90Â° âˆ’ x) = cosec x
• cosec(90Â° âˆ’ x) = sec x

### Trigonometry Formulas Involving Reciprocal Identities

• cosec Î¸ = 1/sin Î¸
• sec Î¸ = 1/cos Î¸
• cot Î¸ = 1/tan Î¸
• sin Î¸ = 1/cosec Î¸
• cos Î¸ = 1/sec Î¸
• tan Î¸ = 1/cot Î¸

### Inverse Trigonometry Formulas

• sin-1Â (-x) = -sin-1Â x
• cos-1Â (-x) = Ï€ – cos-1Â x
• tan-1Â (-x) = -tan-1Â x
• cosec-1Â (-x) = -cosec-1Â x
• sec-1Â (-x) = Ï€ – sec-1Â x
• cot-1Â (-x) = Ï€ – cot-1Â x

### Trigonometry Formulas Involving Triple Angle Identities

• sin 3x = 3sin x – 4sin3x
• cos 3x = 4cos3x – 3cos x
• tan 3x = [3tanx – tan3x]/[1 – 3tan2x]