The point P on the unit circle that corresponds to a real number t is [5/7, 2 square root 6/7] how do you find csc(t)?

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The point P on the unit circle that corresponds to a real number t is [5/7, 2 square root 6/7] how do you find csc(t)?

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Answer 1 · 2018-04-02T00:00:48

$csc t = (7sqrt6)/12$

Explanation:

Coordinates of P:
$P (x = 5/7, y = (2sqrt6)/7)$
we have:
$tan t = y/x = ((2sqrt6)/7)(7/5) = (2sqrt6)/5$
$cot t = 1/(tan t) = 5/(2sqrt6)$
Apply the formula:
$csc^2 t = 1 + cot^2 t = 1 + 25/24 = 49/24$
$csc t = 7/(2sqrt6)$ (because t is in Quadrant 1)
$csc t = (7sqrt6)/12$

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The point P on the unit circle that corresponds to a real number t is [5/7, 2 square root 6/7] how do you find csc(t)?

1 Answer

Explanation:

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