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# Fundamental Identities

Submitted By salvatorewolf
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Fundamental Identities

Reciprocal Identities sin θ = 1csc θ cos θ = 1sec θ

csc θ = 1sin θ sec θ = 1cos θ

tan θ = 1cot θ cot θ = 1tan θ

Quotient Identities tan θ = sinθcos θ cot θ = cosθsin θ

Pythagorean Identities sin2θ + cos2θ = 1 tan2θ + 1 = sec2θ sin2θ = 1 - cos2θ tan2θ = sec2θ – 1 cos2θ = 1 - sin2θ 1 = sec2θ - tan2θ

1 + cot2θ = csc2θ cot2θ = csc2θ – 1
1 = csc2θ - cot2θ

Negative-Angle Identities sin (-θ) = - sin θ cos (-θ) = cos θ csc (-θ) = - csc θ sec (-θ) = sec θ

tan (-θ) = - tan θ cot (-θ) = - cot θ
-------------------------------------------------

-------------------------------------------------

Fundamental Identities

Reciprocal Identities sin θ = 1csc θ cos θ = 1sec θ

csc θ = 1sin θ sec θ = 1cos θ

tan θ = 1cot θ cot θ = 1tan θ

Quotient Identities tan θ = sinθcos θ cot θ = cosθsin θ

Pythagorean Identities sin2θ + cos2θ = 1 tan2θ + 1 = sec2θ sin2θ = 1 - cos2θ tan2θ = sec2θ – 1 cos2θ = 1 - sin2θ 1 = sec2θ - tan2θ

1 + cot2θ = csc2θ cot2θ = csc2θ – 1
1 = csc2θ - cot2θ

Negative-Angle Identities sin (-θ) = - sin θ cos (-θ) = cos θ csc (-θ) = - csc θ sec (-θ) = sec θ

tan (-θ) = - tan θ cot (-θ) = - cot θ
Fundamental Identities

Reciprocal Identities sin θ = 1csc θ cos θ = 1sec θ

csc θ = 1sin θ sec θ = 1cos θ

tan θ = 1cot θ cot θ = 1tan θ

Quotient Identities tan θ = sinθcos θ cot θ = cosθsin θ

Pythagorean Identities sin2θ + cos2θ = 1 tan2θ + 1 = sec2θ sin2θ = 1 - cos2θ tan2θ = sec2θ – 1 cos2θ = 1 - sin2θ 1 = sec2θ - tan2θ

1 + cot2θ = csc2θ cot2θ = csc2θ – 1
1 = csc2θ - cot2θ

Negative-Angle Identities sin (-θ) = - sin θ cos (-θ) = cos θ csc (-θ) = - csc θ sec (-θ) = sec θ

tan (-θ) = - tan θ cot (-θ) = - cot θ
-------------------------------------------------

-------------------------------------------------

Fundamental Identities

Reciprocal Identities sin θ = 1csc θ cos θ = 1sec θ

csc θ = 1sin θ sec θ = 1cos θ

tan θ = 1cot θ cot θ = 1tan θ

Quotient Identities tan θ = sinθcos θ cot θ = cosθsin θ

Pythagorean Identities sin2θ + cos2θ = 1 tan2θ + 1 = sec2θ sin2θ = 1 - cos2θ tan2θ = sec2θ – 1 cos2θ = 1 - sin2θ 1 = sec2θ - tan2θ

1 + cot2θ = csc2θ cot2θ = csc2θ – 1
1 = csc2θ - cot2θ

Negative-Angle Identities sin (-θ) = - sin θ cos (-θ) = cos θ csc (-θ) = - csc θ sec (-θ) = sec θ

tan (-θ) = - tan θ cot (-θ) = - cot θ

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