If csc theta = 8/7, which equation represents (cot theta) ? A. Cot theta=√15/8 B. cot theta=√15 / 7 C. cot theta=7√15 / 15

Question

If csc theta = 8/7, which equation represents (cot theta) ?
A. Cot theta=√15/8
B. cot theta=√15 / 7
C. cot theta=7√15 / 15
D. cot theta= 8√15 / 15

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Mary 2 weeks 2021-09-14T22:13:38+00:00 2 Answers 0

Answers ( )

  1. Emma
    0
    2021-09-14T22:15:00+00:00

    Answer:

    Option B

    Step-by-step explanation:

    just i took the test

    0
    2021-09-14T22:15:35+00:00

    Out of the given choice, the equation represents \cot \theta=\frac{\sqrt{15}}{7}.

    Answer: Option B

    Step-by-step explanation:

    We know, \csc \theta=\frac{1}{\sin \theta}

                    \sin \theta=\frac{1}{\csc \theta}

    Given data:

                    \csc \theta=\frac{8}{7}

    So, now sin theta can express as

                    \sin \theta=\frac{7(\text { opposite })}{8(\text { Hypotenuse })}

    Sin theta defined by the ratio of opposite to the hypotenuse. In general, the adjacent can be calculated by,

               \text {(opposite) }^{2}+(\text { adjacent })^{2}=(\text {Hypotenuse})^{2}

              7^{2}+(\text { adjacent })^{2}=8^{2}

             (\text {adjacent})^{2}=8^{2}-7^{2}=64-49=15

    Taking square root, we get

               \text { adjacent }=\sqrt{15}

    Also, we know the formula for cot theta,

             \cot \theta=\frac{1}{\tan \theta}=\frac{1}{\left(\frac{\sin \theta}{\cos \theta}\right)}=\frac{\cos \theta}{\sin \theta}

    Cos theta denoted as the ratio of adjacent to the hypotenuse.

               \cos \theta=\frac{\sqrt{15}(\text {Adjacent})}{8(\text {Hypotenuse})}

    Therefore, find now as below,

               \cot \theta=\frac{\left(\frac{\sqrt{15}}{8}\right)}{\left(\frac{7}{8}\right)}=\frac{\sqrt{15}}{8} \times \frac{8}{7}=\frac{\sqrt{15}}{7}

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