Trig

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can I please have help with these 3 questions?

1. Solve this equation graphically on the interval [0, 2ð]. list the solutions.

sin(2x)-1=tan x

2. solve sin x cos x= sqrt3/4
3. solve tan^2 x-3tan x+2=0

thank you! show step by step please.

  • Trig -

    1. try
    http://www.wolframalpha.com/input/?i=sin%282x%29-1%3Dtan%28x%29+

    2.
    sinxcosx = √3/4
    times 2
    2sinxcosx = √3/2
    sin(2x) = √3/2
    2x = 60° or 2x = 120°
    x = 30° or x = 60°
    period of sin 2x is 180°
    so other solutions
    x = 30 + k(180) and x = 60 + k(180) degrees , where k is an inter

    in radians:
    x = π/6 + kπ or x = π/3 + kπ


    3. let tanx = t
    you have t^2 - 3t + 2 = 0
    (t-2)(t-1) = 0
    t = 2 or t = -1
    so
    tanx = 2 -----> two answers in domain 0≤x≤2π
    or
    tanx = -1 ---> two answers in domain 0 ≤ x ≤ 2

    give it a try

  • Trig -

    thank you so much!

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