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# Trigonometry Formulas | Sign of Trigonometric Functions in Different Quadrants

June 21, 2022
written by Azhar Ejaz

The branch of mathematics that focuses on relationships between the sides and angles of triangles is called trigonometry. The word trigonometry comes from the Latin derivative of Greek words for the triangle (trigonon) and measure (metron).

As we know without a formula no operation can be performed. Here are important formulas that help the student to solve difficult problems

## Even and odd Formulas

sin(âˆ’Î¸) = âˆ’sin Î¸

cos(âˆ’Î¸) = cos Î¸

tan(âˆ’Î¸) = âˆ’tan Î¸

cosec(âˆ’Î¸) = âˆ’cosecÎ¸

sec(âˆ’Î¸) = sec Î¸

cot(âˆ’Î¸) = âˆ’cot Î¸

## Pythagorean Identities

Sin2 Î¸ = 1- Cos2 Î¸

Sin2 Î¸ + Cos2 Î¸ = 1

Sec2 Î¸ = 1 + Tan2 Î¸

Cosec2 Î¸ = 1+ Cot2 Î¸

sin(Ï€/2-A) = cos A

cos(Ï€/2-A) = sin A

sin(Ï€-A) = sin A

cos(Ï€-A) = -cos A

sin(Ï€+A)=-sin A

cos(Ï€+A)=-cos A

sin(2Ï€-A) = -sin A

cos(2Ï€-A) = cos A

## Sum and difference identities

cos (A + B) = cos A cos B â€“ sin A sin B

cos (A â€“ B) = cos A cos B + sin A sin B

sin (A+B) = sin A cos B + cos A sin B

sin (A -B) = sin A cos B â€“ cos A sin B

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