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Anonymous
Anonymous asked in Science & MathematicsMathematics · 2 months ago

Why is -30 degrees not a solution for sintheta = - 1/2?

3 Answers

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  • 2 months ago

    sinθ = -1/2

    so, θ = sin⁻¹​(-1/2)

    Hence, θ = -30° + 360n° or (180 - (-30))° + 360n°...for n = 0, 1, 2,...

    i.e. θ = -30° ± 360n° or 210° ± 360n°

    so, θ = -30° is a possible solution

    However, when solving trigonometric equations we get an infinite number of possible solutions as sinθ is continuous and periodic every 360°.

    so, if we were asked to solve sinθ = -1/2 for a sspecified domain i.e. 0 ≤ θ ≤ 360° we would have:

    θ = 210° and 330°

    But for -360° ≤ θ ≤ 360° we would have:

    θ = -150°, -30°, 210° and 330°

    :)>

  • ?
    Lv 7
    2 months ago

    It is a solution. Possible sources of thinking it isn't are using radians instead of degrees or being required to give solutions between 0 and 360

  • Bryce
    Lv 7
    2 months ago

    Is there a domain given?  -30° might not be in the given domain; otherwise, it would be a correct solution.

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