Trigonometry

Special angle formulas

0° angle

• 0 radians

• sine 0° = 0

• cosine 0° = 1

• tangent 0° = 0.

30° angle

• π​ ⁄ 6 radians (180° / 6)

• sine 30° = 1​ ⁄ 2

• cosine 30° = √3 ⁄ 2

• tangent 30° = 1​ ⁄ √3

45° angle

• π​ ⁄ 4 radians (180° / 4)

• sine 45° = √2 ⁄ 2

• cosine 45° = √2 ⁄ 2

• tangent 45° = 1​

60° angle

• π​ ⁄ 3 radians (180° / 3)

• sine 60° = √3 ⁄ 2

• cosine 60° = 1 ⁄ 2

• tangent 60° = √3

90° angle

• π​ ⁄ 2 radians (180° / 2)

• sine 90° = 1

• cosine 90° = 0

• tangent 90° undefined

120° angle

• 2π​ ⁄ 3 radians

• 2 × 60°

135° degrees

• 3π​ ⁄ 4 radians

• 3 × 45°

150° degrees

• 5π​ ⁄ 6 radians

• 180° - 30°

180° degrees

• π​ radians

• half circle

Basic Trigonometric Ratio (opp, adj, hyp)

• sin θ =

• cos ⁡θ =

• tan⁡ θ =

• SOH

• CAH

• TOA

Cosecant

• csc θ = ?

1 / sin θ

Secant

• sec θ = ?

1 / cos θ

Cotangent

• cot θ = ?

• 1 / tan θ

• cos θ / sin θ

tan θ = ?

• whats another way to write tangent θ?

sin θ / cos θ

Contangent

• cot θ = ?

• 1 / tan θ

• cos θ / sin θ

Pythagorean Identities

• ? + ? = 1

• 1 + ? = ?

• 1 + ? = ?

• sin² θ + cos² θ = 1

• 1 + tan² θ = sec² θ

• 1 + cot² θ = csc² θ

Quandrant 1

• what is the degree in radians

• which angles are positive in this quandrant?

• 0 to π​ ⁄ 2

• All angles are positive

Quandrant 2

• what is the degree in radians

• which angles are positive in this quandrant?

• π​ ⁄ 2 to π

• Only sin is positive

Quandrant 3

• what is the degree in radians

• which angles are positive in this quandrant?

• π to 3π​ ⁄ 2

• only tan is positive

Quandrant 4

• what is the degree in radians

• which angles are positive in this quandrant?

• 3π​ ⁄ 2 to 2π

• only cos is positive

Even-odd identities

• sin (-θ) = ?

• cos (-θ) = ?

• tan (-θ) = ?

• sin (-θ) = - sin θ

• cos (-θ) = cos θ

• tan (-θ) = - tan θ

Double angle formula for sine

sin 2θ = 2 sinθcosθ

Double angle formula for cosine

• there are 3

• cos 2θ = 2 cos²θ - 1

• cos 2θ = 1 - 2sin²θ

• cos 2θ = cos²θ - sin²θ

Double angle formula for tangent

tan θ = 2 tan θ / (1 - tan² θ)