Identities Flashcards by Ashley Michele | Brainscape

Q

Sine of a Sum

A

sin(A+B) = sin(A)cos(B) + cos(A)sin(B)

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Q

Sine of a Difference

A

sin(A–B) = sin(A)cos(B) – cos(A)sin(B)

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Q

Tangent of a Sum

A

tan(A+B) = tan(A) + tan(B)
1 – tan(A)tan(B)

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Q

Tangent of a Difference

A

tan(A+B) = tan(A) – tan(B)
1 + tan(A)tan(B)

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Q

Cosine of a Sum

A

cos(A+B) = cos(A)cos(B) – sin(A)sin(B)

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Q

Cosine of a Difference

A

cos(A–B) = cos(A)cos(B) + sin(A)sin(B)

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Q

Cofunction Identities

A

cos(90º – θ) = sin(θ)

cot(90º – θ) = tan(θ)

csc(90º – θ) = sec(θ)

ex: csc(35) = sec(55)

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Q

Odd Trig Fuctions

A

cos(-x) = cos(x)

sec(-x) = sec(x)

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Q

Even Trig Functions

A

sin(-x) = -sin(x)

csc(-x) = -csc(x)

tan(-x) = -tan(x)

cot(-x) = -cot(x)

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Q

Pythagorean Identities

(sin/cos)

A

sin²(θ) + cos²(θ) = 1

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Q

Pythagorean Identities

(tan/sec)

A

tan²(θ) + 1 = sec²(θ)

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Q

Pythagorean Identites

(cot/csc)

A

1 + cot²(θ) = csc²(θ)

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Q

Double Angle Identites

(cos2A)

A

cos2(A) = cos²(A) – sin²(A)

cos2(A) = 2cos²(A) – 1

cos2(A) = 1 – 2sin²(A)

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Q

Double Angle Identites

(tan)

A

tan2(A) = 2tan(A)
1 – tan²(A)

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Q

Double Angle Identities

(sin)

A

sin2(A) = 2sin(A)•cos(A)

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Q

Product-to-Sum Identities

(cosAcosB)

A

1/2[cos(A+B) + cos(A–B)]

Q

Product-to-Sum Identities

(sinAsinB)

A

sin(A)sin(B) = 1/2[cos(A–B) – cos(A+B)]

Q

Product-to-Sum Identities

(sinAcosB)

A

sin(A)cos(B) = 1/2[sin(A+B) + sin(A–B)]

Q

Product-to-Sum Identites

(cosAsinB)

A

cos(A)sin(B) = 1/2[sin(A+B) – sin(A–B)]

Q

Sum-to-Product Identites

(sinA + sinB)

A

sin(A)+sin(B) = 2sin((A+B)/2)•cos((A–B)/2)

Q

Sum-to-Product Identites

sin(A) - sin(B)

A

sin(A)–sin(B) = 2cos((A+B)/2)•sin((A–B)/2)

Q

Sum-to-Product Identites

cos(A) + cos(B)

A

cos(A)+cos(B) = 2cos((A+B)/2)•cos((A–B)/2)

Q

Product-to-Sum Identities

cos(A) - cos(B)

A

cos(A)–cos(B) = -2sin((A+B)/2)•sin((A–B)/2)

Q

A