How do you find the exact values of sin(u/2), cos (u/2), tan (u/2) using the half angle formulas given $cos u = \frac{3}{5}$ $cos u= 3/5$ , $0 < u < \frac{π}{2}$ $0<u<pi/2$ ?

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How do you find the exact values of sin(u/2), cos (u/2), tan (u/2) using the half angle formulas given $cos u = \frac{3}{5}$ $cos u= 3/5$ , $0 < u < \frac{π}{2}$ $0<u<pi/2$ ?

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Answer 1 · 2015-05-21T02:02:55

#cos x = 3/5

$2 {cos}^{2} (\frac{x}{2}) = 1 + cos x = 1 + \frac{3}{5} = \frac{8}{5} - \to cos (\frac{x}{2}) = 0.89$ $2cos^2 (x/2) = 1 + cos x = 1 + 3/5 = 8/5 --> cos (x/2) = 0.89$

$2 {sin}^{2} (\frac{x}{2}) = 1 - cos x = 1 - \frac{3}{5} = \frac{2}{5} - \to sin (\frac{x}{2}) = 0.48$ $2sin^2 (x/2) = 1 - cos x = 1 - 3/5 = 2/5 --> sin (x/2) = 0.48$

$tan (\frac{x}{2}) = \frac{sin (\frac{x}{2})}{cos (\frac{x}{2})} = \frac{0.48}{0.89} = 0.54$ $tan (x/2) = sin (x/2)/cos (x/2) = 0.48/0.89 = 0.54$

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How do you find the exact values of sin(u/2), cos (u/2), tan (u/2) using the half angle formulas given $cos u = \frac{3}{5}$ $cos u= 3/5$ , $0 < u < \frac{π}{2}$ $0<u<pi/2$ ?

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How do you find the exact values of sin(u/2), cos (u/2), tan (u/2) using the half angle formulas given $cos u = \frac{3}{5}$ $cos u= 3/5$ , $0 < u < \frac{π}{2}$ $0<u<pi/2$ ?