## Trigonometry Formulas and Identities

Trigonometry Formula is a set of mathematical equations and relationships that are used to solve problems related to angles and sides of triangles. Trigonometry formulas are fundamental tools in the field of trigonometry and are used extensively in various disciplines such as mathematics, physics, engineering, and navigation. All Trigonometry formulas help in calculating the values of unknown angles or sides based on the given information.

The following is a list of all Trigonometry Formulas.

### Tangent and Cotangent Formulas

```         sin θ
tan θ = ———————
cos θ

cos θ
cot θ = ———————
sin θ```

### Even and Odd functions

```sin(-θ)   = - sinθ
cos(-θ)   =   cosθ
tan(-θ)   = - tanθ
cosec(-θ) = - cosecθ
sec(-θ)   =   secθ
cot(-θ)   = - cotθ```

### Reciprocal Identities

```            1
sin θ = —————————
cosec θ

1
cos θ = —————————
sec θ

1
tan θ = —————————
cot θ

1
cosec θ = ———————
sin θ

1
sec θ = ———————
cos θ

1
cot θ = ———————
tan θ

```

### Pythagorean Identities

```sin²θ + cos²θ = 1
1 + tan²θ = sec²θ
1 + cot²θ = cosec²θ```

### Periodic Formulas

```If ‘n’ is an integer, then
sin(θ+2πn) = sinθ
cos(θ+2πn) = cosθ
tan(θ+2πn) = tanθ
cosec(θ+2πn) = cosecθ
sec(θ+2πn) = secθ
cot(θ+2πn) = cotθ```

### Sum and Difference Formulas

```sin(A±B) = sin A cos B ± cos A sin B
cos(A±B) = cos A cos B ± sin A sin B
tan A ± tan B
tan(A±B) = —————————————————
1 ± tan A tan B```

### Product to sum Formulas

```               1
sin A sin B =  — [cos(A-B)-cos(A+B)]
2
1
cos A cos B =  — [cos(A-B)+cos(A+B)]
2
1
sin A cos B =  — [sin(A+B)+sin(A-B)]
2
1
cos A sin B =  — [sin(A+B)-sin(A-B)]
2
```

### Co Function Formulas

```     π
sin(——— - θ) = cos θ
2
π
cos(——— - θ) = sin θ
2
π
tan(——— - θ) = cot θ
2
π
sec(——— - θ) = cosec θ
2
π
cosec(——— - θ) = sec θ
2
π
cot(——— - θ) = tan θ
2
```

### Multiple and Half angles

```1. sin2A = 2sinAcosA

2. cos2A = cos²A - sin²A
= cos²A - 1
= 1 - 2sin²A

2tanA
3. tan2A = ———————————
1 - tan²A

2tanA
4. sin2A = ———————————
1 + tan²A

1 - tan²A
5. cos2A = ———————————
1 + tan²A

6. sin3A = 3sinA - 4sin³A

7. cos3A = 3cos³A - 3cosA

3tanA - tan³A
8. tan3A = ———————————————
1 - 3tan²A```

### Factorization of the Sum or Difference of sine and cosine with two variables

```                       C + D       C - D
1. sinC + sinD = 2sin(———————)cos(———————)
2           2
C + D       C - D
2. sinC - sinD = 2cos(———————)sin(———————)
2           2
C + D       C - D
3. cosC + cosD = 2cos(———————)cos(———————)
2           2
C + D       C - D
4. cosC - cosD = -2sin(———————)sin(———————)
2           2```

### Trigonometry Table

 Angle(Degrees) 0° 30° 45° 60° 90° 120° 135° 150° 180° Angle(Radians) 0 π/6 π/4 π/3 π/2 2π/3 3π/4 5π/6 π sin 0 1/2 1/√2 √3/2 1 √3/2 1/√2 1/2 0 cos 1 √3/2 1/√2 1/2 0 -1/2 -1/√2 -√3/2 -1 tan 0 1/√3 1 √3 ∞ -√3 -1 -1/√3 0 cot ∞ √3 1 1/√3 0 -1/√3 -1 -√3 ∞ sec 1 2/√3 √2 2 ∞ -2 -√2 -2/√3 -1 cosec ∞ 2 √2 2/√3 1 2/√3 √2 2 ∞

## Trigonometry Formula Topics

Trigonometry Formula and Identities

Trigonometry Tangent and Cotangent Formulas

Trigonometry Even and Odd functions

Trigonometry Reciprocal Identities

Trigonometry Pythagorean Identities

Trigonometry Pythagorean Even and Odd functions

Trigonometry Periodic Formulas

Trigonometry Double Angle Formulas

Trigonometry Sum and Difference Formulas

Trigonometry Product to sum Formulas

Trigonometry Co Function Formulas