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If sin(theta)=15/17 and cos(beta)=(-5/13 (both theta and beta are in quadrant II) find tan(theta+beta)

  • Pre-Calculus -

    You should recognize the 8,15,17 and 5,12,13 right-angled triangles

    so in II if
    sinØ= 15/17, then cosØ = -8/17 and tanØ = - 15/8

    cosß = -5/13 , then sinß = 12/13 and tanß = -12/5

    tan(Ø+ß) = (tanØ + tanß)/(1 - tanØtanß)
    = ....

    you finish the arithmetic.

  • Pre-Calculus -

    Ok i understand until you say that tan(theta) +tan(beta) needs to be divided by 1-tan(theta)tan(beta) where does that come from?

  • Pre-Calculus -

    I assumed you knew the formulas, since you have know them to do these kind of problems

    look under "other identities"

  • Pre-Calculus -

    I do but why did u use that one. Im trying to understand because i have a test tomorrow and i have to do well on it.

  • Pre-Calculus -

    well, it asked for tan(Ø+ß) didn't it?

    The letters themselves of course don't matter
    tan(A+B) =(tanA + tanB)/(1- tanAtanB)

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