Trigonometric Identities Flashcards by Evelyn P

Q

Reciprocal Identity
sinu =

A

= 1/cscu

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Q

Reciprocal Identity
cosu =

A

= 1/secu

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Q

Reciprocal Identity
tanu =

A

= 1/cotu

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Q

Reciprocal Identity
cscu =

A

= 1/sinu

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Q

Reciprocal Identity
secu =

A

= 1/cosu

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Q

Reciprocal Identity
cotu =

A

= 1/tanu

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Q

Quotient Identity
tanu =

A

= sinu/cosu

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Q

Quotient Identity
cotu =

A

= cosu/sinu

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Q

Pythagorean Identity
sin^2u + cos^2u =

A

= 1

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Q

Pythagorean Identity
tan^2u + 1 =

A

= sec^2u

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Q

Pythagorean Identity
1+ cot^2u =

A

= csc^2u

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Q

Cofunction Identity
sin(π/2 - u) =

A

= cosu

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Q

Cofunction Identity
cos(π/2 - u) =

A

= sinu

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Q

Cofunction Identity
tan(π/2 - u) =

A

= cotu

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Q

Cofunction Identity
cot(π/2 - u) =

A

= tanu

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Q

Cofunction Identity
csc(π/2 - u) =

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A

= secu

Q

Cofunction Identity
sec(π/2 - u) =

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A

= cscu

Q

Even/Odd Identity
sin(-u) =

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A

= -sinu

Q

Even/Odd Identity
csc(-u) =

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A

= -cscu

Q

Even/Odd Identity
cos(-u) =

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A

= cosu

Q

Even/Odd Identity
sec(-u) =

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A

= secu

Q

Even/Odd Identity
tan(-u) =

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A

= -tanu

Q

Even/Odd Identity
cot(-u) =

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A

= -cotu

Q

Sum & Difference Formula
sin(u +- v) =

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A

= sinucosv +- cosusinv

Sum & Difference Formula cos(u +- v) =

= cosucosv -+ sinusinv

Sum & Difference Formula tan(u +- v) =

= (tanu +- tanv)/(1 -+ tanutanv)

Double-Angle Formula sin2u =

= 2sinucosu

Double-Angle Formula cos2u =

= cos^2u - sin^2u = 2cos^2u - 1 = 1 - 2sin^2u

Double-Angle Formula tan2u =

= (2tanu)/(1 - tan^2u)

Half-Angle Formula sin(u/2) =

= +- √(1 - cosu)/2

Half-Angle Formula cos(u/2) =

= +- √(1 + cosu)/2

Half-Angle Formula tan(u/2) =

= (1 - cosu)/sinu = sinu/(1 + cosu)

Power-Reducing Formula sin^2u =

= (1 - cos2u)/2

Power-Reducing Formula cos^2u =

= (1 + cos2u)/2

Power-Reducing Formula tan^2u =

= (1 - cos2u)/(1 + cos2u)

If a nonvertical line has inclination @ and slope m, then...

m = tan@

Finding an angle between two lines with slopes m1 and m2

tan@ = |(m1 - m2)/(1 + m1m2)|

Distance between the point (x,y) and the line Ax + By + C = 0

d = |Ax1 + By1 + C|/(√A^2 + B^2)