d the exact Solutions of the ien equation, in radians With $$ 0 \leq x

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d the exact Solutions of the ien equation, in radians With $$ 0 \leq x<2 \pi $$. $$ -2 \sin x=1 $$

UpStudy AI · Accepted Answer

Solve the equation $$ -2\sin(x)=1 $$.
Solve the equation by following steps:
- step0: Solve for $$x$$:
  $$-2\sin\left(xight)=1$$
- step1: Multiply both sides:
  $$-2\sin\left(xight)\left(-\frac{1}{2}ight)=1	imes \left(-\frac{1}{2}ight)$$
- step2: Calculate:
  $$\sin\left(xight)=1	imes \left(-\frac{1}{2}ight)$$
- step3: Calculate:
  $$\sin\left(xight)=-\frac{1}{2}$$
- step4: Use the inverse trigonometric function:
  $$x=\arcsin\left(-\frac{1}{2}ight)$$
- step5: Calculate:
  $$\begin{align}&x=\frac{7\pi }{6}\&x=\frac{11\pi }{6}\end{align}$$
- step6: Add the period:
  $$\begin{align}&x=\frac{7\pi }{6}+2k\pi ,k \in \mathbb{Z}\&x=\frac{11\pi }{6}+2k\pi ,k \in \mathbb{Z}\end{align}$$
- step7: Find the union:
  $$x=\left\{ \begin{array}{l}\frac{7\pi }{6}+2k\pi \\frac{11\pi }{6}+2k\pi \end{array}ight.,k \in \mathbb{Z}$$
The exact solutions of the equation $$ -2\sin(x)=1 $$ in radians with $$ 0 \leq x<2\pi $$ are $$ x=\frac{7\pi}{6}+2k\pi $$ and $$ x=\frac{11\pi}{6}+2k\pi $$, where $$ k $$ is an integer.
The solutions are $$ x=\frac{7\pi}{6}+2k\pi $$ and $$ x=\frac{11\pi}{6}+2k\pi $$.

d the exact Solutions of the
ien equation, in radians
With .

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d the exact Solutions of the ien equation, in radians With .