Trigonometry

Find all degree solutions. (Enter your answers as a comma-separated list. Let k be any integer.)
2 cos2 6θ + 3 cos 6θ + 1 = 0

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  1. 2 cos2 6θ + 3 cos 6θ + 1 = 0
    (2cos6θ+1)(cos6θ+1) = 0
    cos6θ = -1/2 or -1

    so,
    6θ = 2π/3 or 4π/3
    θ = π/9+kπ/3 or 2π/9+kπ/3, k=0..5

    6θ = π
    θ = π+kπ/3, k=0..5

    You add kπ/3 since the solutions are (6θ+2π)k

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  2. how would I convert these to degrees?

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  3. why would you want to?
    Ok, if you must, recall that π = 180°

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  4. Thank you. The answer came out to

    20degree + 60degreeK, 30degree + 60 degreeK, 40degree + 60degreek.

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  5. right, but I'd write it as

    (20+60k)°, (30+60k)°, (40+60k)°

    I see you caught my typo.

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  6. Solve the equation for all degree solutions and if
    0° ≤ θ < 360°.
    Do not use a calculator. (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.)
    2 sin θ −

    3
    = 0

    (a) all degree solutions (Let k be any integer.)
    θ =


    (b) 0° ≤ θ < 360°
    θ =

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