How do you find all six trigonometric function of $θ$ $theta$ if the point (12, -5) is on the terminal side of $θ$ $theta$ ?

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How do you find all six trigonometric function of $θ$ $theta$ if the point (12, -5) is on the terminal side of $θ$ $theta$ ?

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Answer 1 · 2017-06-07T03:40:43

t is in Quadrant 4.
$tan t = \frac{y}{x} = - \frac{5}{12}$ $tan t = y/x = - 5/12$
${cos}^{2} t = \frac{1}{1 + {tan}^{2} t} = \frac{1}{1 + \frac{25}{144}} = \frac{144}{169}$ $cos^2 t = 1/(1 + tan^2 t) = 1/(1 + 25/144) = 144/169$
$cos t = \frac{12}{13}$ $cos t = 12/13$ (t is in Quadrant 4)
$sin t = tan t . cos t = (- \frac{5}{12}) (\frac{12}{13}) = - \frac{5}{13}$ $sin t = tan t.cos t = (-5/12)(12/13) = - 5/13$
$cot t = \frac{1}{tan} = - \frac{12}{5}$ $cot t = 1/(tan) = - 12/5$
$sec t = \frac{1}{cos} = \frac{13}{12}$ $sect = 1/(cos) = 13/12$
$csc t = \frac{1}{sin} = - \frac{13}{5}$ $csc t = 1/(sin) = -13/5$

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How do you find all six trigonometric function of $θ$ $theta$ if the point (12, -5) is on the terminal side of $θ$ $theta$ ?

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How do you find all six trigonometric function of θtheta if the point (12, -5) is on the terminal side of θtheta?

1 Answer

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Impact of this question

How do you find all six trigonometric function of $θ$ $theta$ if the point (12, -5) is on the terminal side of $θ$ $theta$ ?