# Thread: 2 questions

1. ## 2 questions

Hi...
I am so sorry for posting so many question but i have an exam soon, and there are some questions that might appear in the exam and i don't know how to solve them
:-(

Thank you all...This is an amazing forum with amazing people.
God bless you all.

2. Originally Posted by rectangle
Hi...

you didn't pick the easy ones ...

$\sin{a} = 5 - 7\cos{a}$

$\sin^2{a} = 25 - 70\cos{a} + 49\cos^2{a}
$

$1 - \cos^2{a} = 25 - 70\cos{a} + 49\cos^2{a}$

$0 = 50\cos^2{a} - 70\cos{a} + 24
$

$0 = 2(5\cos{a}-4)(5\cos{a}-3}$

$\cos{a} = \frac{4}{5}$ ... $a = \arccos\left(\frac{4}{5}\right)$ , $a = 2\pi - \arccos\left(\frac{4}{5}\right)$

$\cos{a} = \frac{3}{5}$ ... $a = \arccos\left(\frac{3}{5}\right)$ , $a = 2\pi - \arccos\left(\frac{3}{5}\right)
$

note that the above solutions are in the interval $[0,2\pi]$

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I'll have to mull over the 2nd problem if I get the time.