Anonymous
Anonymous asked in Science & MathematicsMathematics · 4 months ago

I need help with this math question?

I got tan x=7/24 and cos x= 24/25. However the answers given are both in negative.

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  • Philip
    Lv 6
    4 months ago

    Put (s,c) = (sinx,cosx). s = (7/25), x in (90,180), 2nd quadrant, where s >0 and c < 0.

    (b) c =-(1-s^2)^1/2)=-[1-(7/25)^2]^(1/2)=-[1-(49/625)]^(1/2)= -(1/25)(625-49)^(1/2) =

    -(1/25)(576)^(1/2) = -(24/25). (a) tanx = sinx/cosx = -(7/25)/(24/25) = -(7/24). 

  • 4 months ago

    sinx = 7/25

    Now, sin²x + cos²x = 1  

    so, cos²x = 1 - sin²x

    i.e. cos²x = 1 - (7/25)² => 576/625

    Hence, cosx = ±24/25

    Now, as 90° < x < 180°, x is in quadrant 2 and cosx is negative

    Hence, cosx = -24/25 

    a) tanx => sinx/cosx = (7/25)/(-24/25)

    so, tanx = -7/24

    b) kos x doesn't mean a lot to me, in Malaysian or English

    :)>

  • You're in Q2, so cos(x) and tan(x) will both be negative.

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