Solve the equation for solutions in the interval [0°, 360°). Round to the nearest degree.

Question

asked Jun 3, 2023 161k views

1 Answer

Misantronic · Answer 1 · 2023-06-07T19:24:07+0000

We will have the following:

$\sin (2\theta)=-(1)/(2)\Rightarrow2\theta=2\pi n_1+(7\pi)/(6)$
$\Rightarrow\theta=\pi n_1+(7\pi)/(12)$

Now, we will solve for the following:

$\Rightarrow\pi n_1+(7\pi)/(12)\le2\pi\Rightarrow\pi n_1\le(17\pi)/(12)$
$\Rightarrow n_1\le(17)/(12)$

This value in degrees is:

$(17)/(12)\text{radians}=81.169\text{degrees}$

So, the solution is located in the interval:

$\lbrack0,81\rbrack$