Solve for x 2cos(x + 40 ^ 0) = 1/2 for r 0<= x<=360^ Worth 6 marks

Question

Solve for x

2cos(x + 40 ^ 0) = 1/2 for r 0<= x<=360^

Worth 6 marks

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Sigridomena 5 months 2021-09-04T22:28:27+00:00 1 Answers 0 views 0

Answers ( )

  1. ngockhue
    0
    2021-09-04T22:29:59+00:00
    Reply

    Answer: x = 115.5°

    Step-by-step explanation:

    I suppose that we have the equation:

    2*cos(x + 40°) = 1/2 for 0° < x < 360°

    Let’s solve this.

    First, we isolate the cosine function:

    cos(x + 40°) = (1/2)/2 = 1/4

    cos(x + 40°) = 1/4

    Now we can use the Acos(x) function, remember that:

    Acos(cos(x)) = x

    cos(Acos(x)) = x

    Then if we use this function in both sides, we get:

    Acos( cos(x + 40°)) = Acos(1/4)

    x + 40° = Acos(1/4) = 75.5°

    x = 75.5° + 40° = 115.5°

    x = 115.5°

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