ong>Answer:

SOHCAHTOA

Sin θ = Opposite side / HYPOTENUSE side

Cos θ = ADJACENT side / Hypotenuse side

Tan θ = Opposite side / Adjacent side

Csc θ = Hypotenuse side / Opposite side

Sec θ = Hypotenuse side / Adjacent side

Cot θ = Adjacent side / Opposite side

Reciprocal Trigonometric Identities

Sinθ = 1 / Cosecθ

Cscθ = 1 / Sinθ

Cosθ = 1 / Secθ

Secθ = 1 / Cosθ

Tanθ = 1 / Cotθ

Cotθ = 1 / Tanθ

Other Trigonometric Identities

Sin²θ + Cos²θ = 1

Sin²θ = 1 - Cos²θ

Cos²θ = 1 - Sin²θ

Sec²θ - Tan²θ = 1

Sec²θ = 1 + Tan²θ

Tan²θ = Sec²θ - 1

Csc²θ - Cot²θ = 1

Csc²θ = 1 + Cot²θ

Cot²θ = Csc²θ - 1

Double Angle Identities

Sin2A = 2 ⋅ SinA ⋅ CosA

Cos2A = Cos²A - Sin²A

Tan2A = 2 ⋅ TanA / (1 - Tan²A)

Cos2A = 1 - 2 ⋅ Sin²A

Cos2A = 2 ⋅ Cos²A - 1

Sin2A = 2 ⋅ TanA / (1 + Tan²A)

Cos2A = (1 - Tan²A) / (1 + Tan²A)

Sin²A = (1 - Cos2A) / 2

Cos²A = (1 + Cos2A) / 2

Half Angle Identities

SinA = 2 ⋅ Sin(A/2) ⋅ Cos(A/2)

CosA = Cos²(A/2) - Sin²(A/2)

TanA = 2 ⋅ Tan(A/2) / [1 - Tan²(A/2)]

CosA = 1 - 2 ⋅ Sin²(A/2)

CosA = 2 ⋅ Cos²(A/2) - 1

SinA = 2 ⋅ Tan(A/2) / [1 + Tan²(A/2)]

CosA = [1 - Tan²(A/2)] / [1 + Tan²(A/2)]

Sin²A/2 = (1 - Cos A) / 2

Cos²A/2 = (1 + Cos A) / 2

Tan²(A/2) = (1 - CosA) / (1 + CosA)

Compound Angles Identities

Sin(A + B) = SinA ⋅ CosB + CosA ⋅ SinB

Sin(A + B) = SinA ⋅ CosB + CosA ⋅ SinB

Cos(A + B) = CosA ⋅ CosB - SinA ⋅ SinB

Cos(A - B) = CosA ⋅ CosB + SinA ⋅ SinB

Tan(A + B) = [TanA + TanB] / [1- TanA ⋅ TanB]

Tan(A - B) = [TanA - TanB] / [1 + TanA ⋅ TanB]

Sum to PRODUCT Identities

SinC + SinD = 2 ⋅ Sin[(C+D) / 2] ⋅ cos [(C-D) / 2]

SinC - SinD = 2 ⋅ Cos [(C+D) / 2] ⋅ Sin [(C-D) / 2]

Step-by-step EXPLANATION:

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