The line y=3x creates an acute angle theta when it crosses the x-axis, Find the exact value of sec theta

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The line y=3x creates an acute angle theta when it crosses the x-axis, Find the exact value of sec theta

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Thiên Hương 5 months 2021-08-25T18:39:13+00:00 1 Answers 62 views 0

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    2021-08-25T18:41:10+00:00

    Answer:

    Sec(θ) = 3

    Step-by-step explanation:

    First, we know that:

    Sec(x) = 1/Cos(x)

    Now we have an angle θ in the intersection between the line y = 3x and the x-axis.

    Here we can think of this as a triangle rectangle, such that:

    x is the adjacent cathetus to θ

    y is the opposite cathetus to θ

    y = 3*x is the hypotenuse.

    Here we also need to remember the relation:

    Cos(θ) = (adjacent cathetus)/(hypotenuse)

    Then we will get:

    Cos(θ) = x/(3*x) = 1/3

    If we multiply both sides by 3, we get:

    Cos(θ)*3 = (1/3)*3 = 1

    Cos(θ)*3 = 1

    Now we can divide both sides by Cos(θ)

    [Cos(θ)*3]/Cos(θ) = 1/Cos(θ)

    3 = 1/Cos(θ)

    And  1/Cos(θ) = Sec(θ)

    Then:

    3 = Sec(θ)

    The exact value of sec theta is 3.

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