you didn't pick the easy ones ...
$\displaystyle \sin{a} = 5 - 7\cos{a}$
$\displaystyle \sin^2{a} = 25 - 70\cos{a} + 49\cos^2{a}
$
$\displaystyle 1 - \cos^2{a} = 25 - 70\cos{a} + 49\cos^2{a}$
$\displaystyle 0 = 50\cos^2{a} - 70\cos{a} + 24
$
$\displaystyle 0 = 2(5\cos{a}-4)(5\cos{a}-3}$
$\displaystyle \cos{a} = \frac{4}{5}$ ... $\displaystyle a = \arccos\left(\frac{4}{5}\right)$ , $\displaystyle a = 2\pi - \arccos\left(\frac{4}{5}\right)$
$\displaystyle \cos{a} = \frac{3}{5}$ ... $\displaystyle a = \arccos\left(\frac{3}{5}\right)$ , $\displaystyle a = 2\pi - \arccos\left(\frac{3}{5}\right)
$
note that the above solutions are in the interval $\displaystyle [0,2\pi]$
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I'll have to mull over the 2nd problem if I get the time.