I WILL MAKE YOU BRAINLIEST! 46 POINTS!!!!! PLEASE HURRY! BRAINLIEST, THANKS, AND 5 STARS! PROMISE!

1 answer:

6 0

A ray is a simple way to show all the solutions to an inequality. When an inequality represents a practical problem, some of the points may not make sense as solutions.

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3 years ago

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Svetach [21]

$\bf sin^2(2\theta)-7sin(2\theta)-1=0\\\\
-------------------------------\\\\
sin(2\theta)=\cfrac{7\pm\sqrt{49-4(1)(-1)}}{2(1)}\implies sin(2\theta)=\cfrac{7\pm\sqrt{49+4}}{2}
\\\\\\
sin(2\theta)=\cfrac{7\pm\sqrt{53}}{2}\implies 2\theta=sin^{-1}\left( \frac{7\pm\sqrt{53}}{2} \right)
\\\\\\
\theta=\cfrac{sin^{-1}\left( \frac{7\pm\sqrt{53}}{2} \right)}{2}$

but anyway, the numerator will give the angles, and θ is just half of each

$\bf \theta=\cfrac{sin^{-1}\left( \frac{7\pm\sqrt{53}}{2} \right)}{2}\\\\
-------------------------------\\\\
sin^{-1}\left( \frac{7+\sqrt{53}}{2} \right)\implies sin^{-1}(7.14)\impliedby \textit{greater than 1, no good}
\\\\\\
sin^{-1}\left( \frac{7-\sqrt{53}}{2} \right)\implies sin^{-1}(-0.14) \approx -8.05^o
\\\\\\
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ok... that's a negative tiny angle, is in the 4th quadrant, if we stick to the range given, from 0 to 360, so we have to use the positive version of it, 360-4.025

so the angle is 355.975°

now, the 3rd quadrant has another angle whose sine is negative, so... if we move from the 180° line down by 4.025, we end up at 184.025°

and those are the only two angles, because, on the 2nd and 1st quadrants, the sine is positive, so it wouldn't have an angle there

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3 years ago