Find the value of the six trigonometric functions of an angle in standard position if the point with coordinates (12,5) lies on its terminal

Question

Find the value of the six trigonometric functions of an angle in standard position if the point with coordinates (12,5) lies on its terminal side

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Clara 1 day 2021-11-25T17:57:50+00:00 1 Answer 0 views 0

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    2021-11-25T17:59:24+00:00

    Answer:

    See explanation

    Step-by-step explanation:

    Point with coordinates (12,5) lies on the distance

    d=\sqrt{(12-0)^2 +(5-0)^2}=\sqrt{144+25}=13

    from the origin.

    Consider right triangle with vertices at the origin, at the given point (12,5) and at it projection on the x- axis (point (12,0)).

    Hence,

    Hypotenuse = 13 units

    Adjacent to the angle leg = 12 units

    Opposite to the angle leg = 5 units

    By the definition of trigonometric functions,

    \sin \theta=\dfrac{\text{Opposite leg}}{\text{Hypotenuse}}=\dfrac{5}{13}\\ \\\cos \theta=\dfrac{\text{Adjacent leg}}{\text{Hypotenuse}}=\dfrac{12}{13}\\ \\\tan \theta=\dfrac{\text{Opposite leg}}{\text{Adjacent leg}}=\dfrac{5}{12}\\ \\\cot \theta=\dfrac{\text{Adjacent leg}}{\text{Opposite leg}}=\dfrac{12}{5}\\ \\\csc \theta=\dfrac{\text{Hypotenuse}}{\text{Opposite leg}}=\dfrac{13}{5}\\ \\\sec \theta=\dfrac{\text{Hypotenuse}}{\text{Adjacent leg}}=\dfrac{13}{12}

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45:7+7-4:2-5:5*4+35:2 =? ( )