HELP ASAP I WILL GIVE BRAINLIST If sin ∅ = -sqrt{3} OVER 2 and π < ∅ < 3π OVER 2, what are the values of cos ∅ and tan ∅?

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HELP ASAP I WILL GIVE BRAINLIST

If sin ∅ = -sqrt{3} OVER 2 and π < ∅ < 3π OVER 2, what are the values of cos ∅ and tan ∅? What is ∅ in degrees and radians? Be sure to show and explain all work.

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Hồng Cúc 3 years 2021-08-02T03:30:20+00:00 1 Answers 15 views 0

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  1. ngocdiep
    0
    2021-08-02T03:31:53+00:00
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    Step-by-step explanation:

    sin ∅ = -(√3)/2

    Note that

    cos²∅ + sin²∅ = 1

    cos²∅ = 1 – sin²∅

    = 1 – (-√3 / 2)²

    = 1 – (-√3)²/ 2²

    = 1 – 3/4

    = 1/4

    cos²∅ = 1/4

    Taking square root of both sides

    cos∅ = 1/2

    Note that tan∅ = sin∅/cos∅

    therefore, tan∅ = -(√3)/2 ÷ 1/2

    = -(√3)/2 × 2/1

    = -√3

    tan∅ = -√3

    Since sin∅ = -√3 /2

    Then ∅ = -60⁰

    The value of ∅ for the given range (third quadrant) is 240⁰.

    NB: sin∅ = sin(180-∅)

    Also, since 180⁰ is π radians, then ∅ = 4π/3

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