given that sin(x+4)=cos(3x)find tan(x+40)to 4 s.f.​

Question

given that sin(x+4)=cos(3x)find tan(x+40)to 4 s.f.​

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Diễm Kiều 4 years 2021-08-27T21:22:00+00:00 1 Answers 3 views 0

Answers ( )

  1. thienthanh
    0
    2021-08-27T21:23:41+00:00
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    Answer:

    \tan(x + 40) = 1.842

    Step-by-step explanation:

    Given

    \sin(x + 4) = \cos(3x)

    Required

    Find \tan(x + 40)

    In trigonometry

    If \sin(A) = \cos(B)

    Then: A + B = 90

    So, we have:

    \sin(x + 4) = \cos(3x)

    3x + x + 4 = 90

    4x + 4 = 90

    Collect like terms

    4x =- 4 + 90

    4x =86

    Solve for x

    x = 86/4

    x = 21.5

    So:

    \tan(x + 40) = \tan(21.5+40)

    \tan(x + 40) = \tan(61.5)

    Using a calculator:

    \tan(x + 40) = 1.842

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