$$ \begin{array}{l}\text { Solve the equation for } \mathrm{x} \text {, where } \mathrm{x} \text { is restricted to the given interval. } \ y=9 \cos \mathrm{x}, \text { for } \mathrm{x} \text { in }[0, \pi]\end{array} $$ $$ \begin{array}{l}\mathrm{x}=\square \ \text { (Use integers or fractions for any numbers in the expression.) }\end{array} $$

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UpStudy AI · Accepted Answer

Solve the equation $$ 9\cos(x)=0 $$.
Solve the equation by following steps:
- step0: Solve for $$x$$:
  $$9\cos\left(xight)=0$$
- step1: Multiply both sides:
  $$9\cos\left(xight)	imes \frac{1}{9}=0	imes \frac{1}{9}$$
- step2: Calculate:
  $$\cos\left(xight)=0	imes \frac{1}{9}$$
- step3: Calculate:
  $$\cos\left(xight)=0$$
- step4: Use the inverse trigonometric function:
  $$x=\arccos\left(0ight)$$
- step5: Calculate:
  $$x=\frac{\pi }{2}$$
- step6: Add the period:
  $$x=\frac{\pi }{2}+k\pi ,k \in \mathbb{Z}$$
The solution to the equation $$9\cos(x)=0$$ is $$x=\frac{\pi}{2}+k\pi$$, where $$k$$ is an integer.

Since the interval is $$[0, \pi]$$, the only solution within this interval is $$x=\frac{\pi}{2}$$.
$$ x=\frac{\pi}{2} $$

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