Problem

Find two values of $0,0 \leq 0<2 \pi$, that satisfy the following equation. \[ \cos \theta=-\frac{\sqrt{2}}{2} \]

Solution

Step 1 :Find two values of \(0,0 \leq 0<2 \pi\), that satisfy the following equation. \[\cos \theta=-\frac{\sqrt{2}}{2}\]

Step 2 :The cosine function has a value of \(-\frac{\sqrt{2}}{2}\) at two points in the interval \([0, 2\pi)\), namely at \(\frac{3\pi}{4}\) and \(\frac{5\pi}{4}\). These are the two solutions to the equation.

Step 3 :Final Answer: The two values of \(\theta\) that satisfy the equation \(\cos \theta=-\frac{\sqrt{2}}{2}\) are \(\boxed{\frac{3\pi}{4}}\) and \(\boxed{\frac{5\pi}{4}}\).

From Solvely APP
Source: https://solvelyapp.com/problems/20733/

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