Mathematical Formulas for Industrial and Mechanical Engineering

Cofunction Identities

sin



π

2

2 u



5 cos u cos



π

2

2 u



5 sin u

tan



π

2

2 u



5 cot u cot



π

2

2 u



5 tan u

sec



π

2

2 u



5 csc u csc



π

2

2 u



5 sec u

Pythagorean Identities

1. sin

2

θ 1 cos

2

θ 5 1

2. tan

2

θ 1 1 5 sec

2

θ

3. cot

2

θ 1 1 5 csc

2

θ

Sum and Difference of Angle Identities

1. sin(α 1 β) 5 sin α cos β 1 cos α sin β

2. sin(α 2 β) 5 sin α cos β 2 cos α sin β

3. cos(α 1 β) 5 cos α cos β 2 sin α sin β

4. cos(α 2 β) 5 cos α cos β 1 sin α sin β

5. tanðα 1 βÞ5

tan α 1 tan β

1 2 tan α tan β

6. tanðα 2 βÞ5

tan α 2 tan β

1 1 tan α tan β

Double Angle Identities

1. sin(2θ) 5 2sin θ cos θ

cosð2θÞ5 cos

2

θ 2 sin

2

θ

5 2 cos

2

2 1

5 1 2 2 sin

2

θ

3. tanð2θÞ5

2 tan θ

1 2 tan

2

θ

Half Angle Identities

1. sin

θ

2

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