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Math Help - Trig help solving.

  1. #1
    Junior Member
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    Trig help solving.

    Solve giving values of theta from 0 to 360 degrees inclusive
    1. 2sinx-cosecx=1
    2. 2 tan(theta/2)+ 3 tan theta=0

    Solve giving values of x from 0 to 2 pi inclusive:

    1. tan2theta+ tantheta=0
    2. 2cosec2theta=1 + tan^2

    thanks if you can help
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  2. #2
    Super Member

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    Lexington, MA (USA)
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    Hello, Confuzzled!

    Here's the first one . . .


    Solve for 0° ≤ x ≤ 360°

    1) .2·sin x - csc x .= .1

    Multiply through by sin x: . 2·sin²x - 1 .= .sin x

    We have: . 2·sin²x - sin x - 1 .= .0

    which factors: . (sin x - 1)(2·sin x + 1) .= .0

    and has these roots:

    . . sin x - 1 .= .0 . . sin x = 1 . . x = 90°

    . . 2·sinx + 1 .= .0 . . sin x = -½ . . x .= .210°, 330°



    2) .2·tan(x/2)+ 3 tan x .= .0

    Using a double-angle identity, we have:

    . . . . . . . . . . . . . .2·tan(x/2)
    . . 2·tan(x/2) + 3 ---------------- .= .0
    . . . . . . . . . . . . .1 - tan²(x/2)

    This simplifies to: .2·tan³(x/2) - 8·tan(x/2) .= .0

    which factors: . 2·tan(x/2) [tan²(x/2) - 4] .= .0

    and has these roots:

    . . 2·tan(x/2) = 0 . . x/2 .= .0°, 180° . . x .= .0°, 360°

    . . tan²(x/2) = 4 . . tan(x/2) = ±2 . . x. = .2·arctan(±2) . .126.9°, 233.1°

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