Trigonometric Identities Flashcards by Jane Baymar | Brainscape

Q

sinθ (Reciprocal)

A

1/cscθ

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Q

cosθ (Reciprocal)

A

1/secθ

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Q

tanθ (Reciprocal)

A

1/cotθ

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Q

cscθ (Reciprocal)

A

1/sinθ

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Q

cotθ (Reciprocal)

A

1/tanθ

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Q

tanθ (Quotient)

A

sinθ/cosθ

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Q

cotθ (Quotient)

A

cosθ/sinθ

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Q

sin^2θ + cos^2θ (Pythagorean)

A

1

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Q

tan^2θ + 1 (Pythagorean)

A

sec^2θ

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Q

cot^2θ + 1 (Pythagorean)

A

csc^2θ

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Q

sinθ (Cofunction)

A

cos(π/2-θ)

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Q

cscθ (Cofunction)

A

sec(π/2-θ)

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Q

tanθ (Cofunction)

A

cot(π/2-θ)

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Q

cosθ (Cofunction)

A

sin(π/2-θ)

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Q

secθ (Cofunction)

A

csc(π/2-θ)

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Q

cotθ (Cofunction)

A

tan(π/2-θ)

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Q

sin(-θ) (Even-Odd)

A

-sinθ

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Q

cos(-θ) (Even-Odd)

A

cosθ

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Q

tan(-θ) (Even-Odd)

A

-tanθ

Q

csc(-θ) (Even-Odd)

A

-cscθ

Q

sec(-θ) (Even-Odd)

A

secθ

Q

cot(-θ) (Even-Odd)

A

-cotθ

Q

sin(A+B) (Sum of Angles)

A

sinA * cosB + cosA * sinB

Q

cos(A+B) (Sum of Angles)

A

cosA * cosB - sinA * sinB

Q

tan(A+B) (Sum of Angles)

A

(tanA + tanB)/(1 - tanA*tanB)

Q

sin(A-B) (Difference of Angles)

A

sinA * cosB - cosA * sinB

Q

cos(A-B) (Difference of Angles)

A

cosA * cosB + sinA * sinB

Q

tan(A-B) (Difference of Angles)

A

(tanA - tanB)/(1 + tanA*tanB)

Q

sin2θ (Double-Angle)

A

2sinθ * cosθ

Q

cos2θ (Double-Angle)

A

cos^2θ - sin^2θ
1 - 2sin^2θ
2cos^θ -1

Q

tan2θ (Double-Angle)

A

(2tanθ)/(1-tan^2θ)

Q

sin(θ/2) (Half-Angle)

A

+/- sqrt((1-cosθ)/2)

Q

cos(θ/2) (Half-Angle)

A

+/- sqrt((1+cosθ)/2)

Q

tan(θ/2) (Half-Angle)

A

+/- sqrt((1-cosθ)/(1+cosθ))
(1-cosθ)/(sinθ)
(sinθ)/(1+cosθ)

Q

sin^2θ (Power-Reducing)

A

(1-cos2θ)/2

Q

cos^2θ (Power-Reducing)

A

(1+cos2θ)/2

Q

tan^2θ (Power-Reducing)

A

(1-cos2θ)/(1+cos2θ)

Q

sinA * sinB (Product-to-Sum)

A

1/2[cos(A-B) - cos(A+B)]

Q

cosA * cosB (Product-to-Sum)

A

1/2[cos(A-B) + cos(A+B)]

Q

sinA * cosB (Product-to-Sum)

A

1/2[sin(A-B) + sin(A-B)]

Q

cosA * sinB (Product-to-Sum)

A

1/2[sin(A+B) - sin(A-B)]

Q

sinA + sinB (Sum-to-Product)

A

2 * sin(A+B/2) * cos(A-B/2)

Q

cosA + cosB (Sum-to-Product)

A

2 * cos(A+B/2) * cos(A-B/2)

Q

sinA - sinB (Sum-to-Product)

A

2 * cos(A+B/2) * sin(A-B/2)

Q

cosA - cosB (Sum-to-Product)

A

-2 * sin(A+B/2) * sin(A-B/2)

Q

secθ (Reciprocal)

A

1/cosθ