How do you find the sin(Θ) of an angle in standard position if the terminal side passes through the point (4, -8)?

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How do you find the sin(Θ) of an angle in standard position if the terminal side passes through the point (4, -8)?

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Answer 1 · 2017-03-12T22:40:39

$- \frac{2 \sqrt{5}}{5}$ $- (2sqrt5)/5$

Explanation:

Call t the angle that is in Quadrant 4.
$tan t = - \frac{8}{4} = - 2$ $tan t = -8/4 = - 2$
Use trig identity:
${cos}^{2} t = \frac{1}{1 + {tan}^{2} t} = \frac{1}{1 + 4} = \frac{1}{5}$ $cos^2 t = 1/(1 + tan^2 t) = 1/(1 + 4) = 1/5$
$cos t = \pm \frac{1}{\sqrt{5}}$ $cos t = +- 1/sqrt5$
Because t is in Quadrant 4, then, cos t is positive.
$sin t = cos t . tan t = (\frac{1}{\sqrt{5}}) (- 2) = - \frac{2}{\sqrt{5}} = - \frac{2 \sqrt{5}}{5}$ $sin t = cos t.tan t = (1/sqrt5)(-2) = -2/sqrt5 = - (2sqrt5)/5$

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How do you find the sin(Θ) of an angle in standard position if the terminal side passes through the point (4, -8)?

1 Answer

Explanation:

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