How do you find the exact values of sin 2u, cos 2u, and tan 2u using the double-angle formulas?

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How do you find the exact values of sin 2u, cos 2u, and tan 2u using the double-angle formulas?

sin u= -4/5, 3 $π$ $pi$ /2 < u < 2 $π$ $pi$

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Answer 1 · 2018-06-23T22:20:26

$sin 2 u = - \frac{12}{25}$ $sin 2u = - 12/25$
$cos 2 u = - \frac{9}{15}$ $cos 2u = -9/15$
$tan 2 u = \frac{4}{5}$ $tan 2u = 4/5$

Explanation:

$sin u = - \frac{4}{5}$ $sin u = -4/5$ , and u lies in Quadrant 4.
${cos}^{2} u = 1 - {sin}^{2} u = 1 - \frac{16}{25} = \frac{9}{25}$ $cos^2 u = 1 - sin^2 u = 1 - 16/25 = 9/25$
$cos u = \frac{3}{5}$ $cos u = 3/5$ (cos u is positive because u lies in Q.4)
$sin 2 u = 2 sin u . cos u = (- \frac{4}{5}) (\frac{3}{5}) = - \frac{12}{25}$ $sin 2u = 2sin u.cos u = (-4/5)(3/5) = - 12/25$
${cos}^{2} 2 u = 1 - {sin}^{2} 2 u = 1 - \frac{144}{225} = \frac{81}{225}$ $cos^2 2u = 1 - sin^2 2u = 1 - 144/225 = 81/225$
$cos 2 u = - \frac{9}{15}$ $cos 2u = - 9/15$
(cos 2u is negative because u = - 53.13, so, 2u lies in Quadrant 3)
$tan 2 u = \frac{sin 2 u}{cos 2 u} = \frac{- \frac{12}{25}}{- \frac{15}{9}} = \frac{4}{5}$ $tan 2u = (sin 2u)/(cos 2u) = (-12/25)/(-15/9) = 4/5$

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How do you find the exact values of sin 2u, cos 2u, and tan 2u using the double-angle formulas?

sin u= -4/5, 3 $π$ $pi$ /2 < u < 2 $π$ $pi$

1 Answer

Explanation:

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Science

Math

Humanities

... and beyond

How do you find the exact values of sin 2u, cos 2u, and tan 2u using the double-angle formulas?

sin u= -4/5, 3piπpi/2 < u < 2piπpi

1 Answer

Explanation:

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sin u= -4/5, 3 $π$ $pi$ /2 < u < 2 $π$ $pi$