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Calculate the value of $\sin a+\cos a$, knowing that $\sin a\cos a=0.48$ and $a$ belongs to $\left[\pi; \frac{3\pi}{2}\right]$?

What I did is: $$\sin a \cos a=0.48\ \ |\times 2$$

$$\sin 2a=0.96$$

$a= \dfrac{\arcsin \frac{24}{25}}{2} + \pi n$ or $a=\dfrac{\pi-\arcsin \frac{24}{25}}{2} + \pi n$

Now I don't know how to choose the right angles that belongs to the interval from the condition of the exercise! Thank you in advance!

Siminore
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wonderingdev
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  • http://meta.math.stackexchange.com/questions/5020/mathjax-basic-tutorial-and-quick-reference May help to make your question a bit easier to read – Ahrz Mar 12 '14 at 14:10
  • Use:$$(\sin{a}+\cos{a})^2=(\sin^2{a}+2\sin{a}\cos{a}+\cos^2{a})=1+2(0.48)$$ to find the value of $\sin{a}+\cos{a}$. Also observe that there are two roots, which only one of will fit the criteria of the interval given – user130512 Mar 12 '14 at 14:10

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