If $sin u = - \frac{12}{37}$ $Sin u= -12/37$ and $cos v = - \frac{99}{101}$ $cos v=-99/101$ , with u being in QIII and v being in QII, how do you find the exact value of sin(u-v)?

Question

2242 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-06-04T03:00:23

Use the trig identity: sin (u - v) = sin u.cos v - sin v.cos u

$sin u = - \frac{12}{37}$ $sin u = -12/37$ -> #cos^2 u = 1 - sin^2 u = 1 - 144/1369 = 1225/1369 =

0.89 -> cos u = -0.94# (Q. III)

$cos v = - \frac{99}{101} \to {sin}^{2} v = 1 - {cos}^{2} v = 1 - \frac{9801}{10201} =$ $cos v = -99/101 -> sin^2 v = 1 - cos^2 v = 1 - 9801/10201 =$

$\frac{2400}{10201} = 0.24 \to sin v = 0.49 .$ $2400/10201 = 0.24 -> sin v = 0.49.$ (Q. II)

$sin (u - v) = (- \frac{12}{37}) (- \frac{99}{101}) - (0.94) (0.49) =$ $sin (u - v) = (-12/37)(-99/101) - (0.94)(0.49) =$

$= \frac{1188}{3737} - 0.46 = 0.32 - 0.46 = - 0.14$ $= 1188/3737 - 0.46 = 0.32 - 0.46 = -0.14$

If sinu=−1237Sin u= -12/37 and cosv=−99101cos v=-99/101, with u being in QIII and v being in QII, how do you find the exact value of sin(u-v)?