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A few more trig problems ( Sin(α + β), etc. )

  1. Apr 23, 2009 #1
    1. The problem statement, all variables and given/known data

    Suppose sinα = 4/5 and tanβ= -3/4 where π/2 < α < β < π (pi)

    Find:

    Sin(α + β)

    Cos(α + β)

    Tan(α + β)

    Sin2α

    Cos2β

    Tan2α

    3. The attempt at a solution

    What i have been doing is figuring out the other trig functions

    They gave me sinα=4/5 and tanβ=-3/4

    from that i found cosα=3/5 tanα=3/4 and sinβ=-3/5 cosβ=4/5

    I tried problem a

    sin(α+β)=sinαcosβ+cosαsinβ

    sin(α+β)=4/5 * 4/5 + 3/5 * -3/5

    which gives me 7/25 but I'm not sure I am doing this right... what is the whole (π/2 < α < β < π) thing about am I supposed to be finding points on the unit circle or something? =/
     
  2. jcsd
  3. Apr 23, 2009 #2
    The whole "π/2 < α < β < π (pi)" thing refers to the quadrant the terminal sides of angles α and β are in. So what quadrant is this? And how does this affect the evaluation of the trig functions? Because none of these:
    are correct.


    01
     
    Last edited: Apr 23, 2009
  4. Apr 23, 2009 #3
    ahh Ok so it's in the second quadrant which makes the x negative and the y positive

    so would that make

    cosα=-3/5 tanα=-3/4 and sinβ=-3/5 cosβ=4/5

    is this right?
     
  5. Apr 23, 2009 #4

    Mark44

    Staff: Mentor

    From your given condition, both alpha and beta are in the 2nd quadrant, so how can sin(beta) be negative and how can cos(beta) be positive? If you have these wrong, you are liable to have the others (the tangents) wrong, too.
     
  6. Apr 23, 2009 #5
    So would it be cosα = -3/5 tanα = -3/4 and sinβ = +3/5 cosβ = -4/5
     
  7. Apr 24, 2009 #6
    Almost. The signs are correct, but double check tan α.


    01
     
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