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Math Help - Trigonometric Identities

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    Lightbulb Trigonometric 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.?
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    Quote Originally Posted by Pajkaj View Post
    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.?

    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))
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Pajkaj View Post
    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.?
    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
    Attached Thumbnails Attached Thumbnails Trigonometric Identities-tri2.gif  
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