My teacher was sick the day we learned the trig identities in class and I can't seem to find them in my text book - can someone post the oh say ten or so basic ones I should for sure know? Double angle functions, pythag ones, etc.?:confused:

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- Mar 18th 2007, 11:56 AMPajkajTrigonometric Identities
My teacher was sick the day we learned the trig identities in class and I can't seem to find them in my text book - can someone post the oh say ten or so basic ones I should for sure know? Double angle functions, pythag ones, etc.?:confused:

- Mar 18th 2007, 12:08 PMJhevon

sin^2(x) + cos^2(x) = 1

tan(x) = sin(x)/cos(x)

sec^2(x) = 1 + tan(x)

csc^2(x) = 1 + cot^2(x)

sec(x) = 1/cos(x)

csc(x) = 1/sin(x)

cot(x) = 1/tan(x) = cos(x)/sin(x)

Addtion and subtraction formulas:

sin(A + B) = sinAcosB + sinBcosA

sin(A - B) = sinAcosB - sinBcosA

cos(A + B) = cosAcosB - sinAsinB

cos(A - B) = cosAcosB + sinAsinB

tan(A + B) = (tanA + tanB)/(1 - tanAtanB)

tan(A - B) = (tanA - tanB)/(1 + tanAtanB)

the tan formulas are not as important to memorize, you can use the identity tan(x) = sin(x)/cos(x) to find them if necessary

Double angle formulas:

for these, you just apply the addtion formulas for two angles being the same.

sin(2A) = sin(A + A) = sinAcosA + sinAcosA = 2sinAcosA

cos(2A) = cos(A + A) = cosAcosA - sinAsinA = cos^2(A) - sin^2(A)

remember, sin^2(A) + cos^2(A) = 1

so sin^2(A) = 1 - cos^2(A) and,

cos^2(A) = 1 - sin^2(A)

so cos(2A) = 1 - sin^2(A) - sin^2(A) = 1 - 2sin^2(A)

or cos(2A) = cos^2(A) - (1 - cos^2(A)) = 2cos^2(A) - 1

tan(2A) = 2tanA/(1 - tan^2(A)) - Mar 18th 2007, 12:14 PMJhevon
for pythogorian identities, see diagram.

sin(x) = opp/hyp

cos(x) = adj/hyp

tan(x) = opp/adj = sin(x)/cos(x)

sec(x) = 1/cos(x) = hyp/adj

csc(x) = 1/sin(x) = hyp/opp

cot(x) = 1/tan(x) = cos(x)/sin(x) = adj/opp

a mnemonic to remember these (which I never use but other people seem to find it helpful) is:

SOHCAHTOA

meanng

Sine is Opposite over Hypotenuse Cosine is Adjacent over Hypotenuse Tangent is Oposite over Adjacent