is this answer wrong?trig

oxrigby · #1 $Old$ October 15th, 2008, 02:04 PM

Q find in radians, all the values of $\theta$ between $-\pi and \pi$ satisfying the equation

$8cos^2\theta+2sin\theta=7$

the answers are 0.524 2.261 which i get but i dont get 3.386 or 6.034 instead i get -14.5 degrees and hence 180-14.5 can any see where I have gone wrong or is it the answers thnx.!

skeeter · #2 $Old$ October 15th, 2008, 06:14 PM

$8\cos^2{\theta} + 2\sin{\theta} = 7$

$8(1 - \sin^2{\theta}) + 2\sin{\theta} = 7$

$8 - 8\sin^2{\theta} + 2\sin{\theta} = 7$

$0 = 8\sin^2{\theta} - 2\sin{\theta} - 1$

$0 = (4\sin{\theta} + 1)(2\sin{\theta} - 1)$

$\sin{\theta} = -\frac{1}{4}$

${\theta} = \arcsin\left(-\frac{1}{4}\right)$

${\theta} = -\left[\pi + \arcsin\left(-\frac{1}{4}\right)\right]$

$\sin{\theta} = \frac{1}{2}$

$\theta = \frac{\pi}{6}$

$\theta = \frac{5\pi}{6}$