chapter 6 quiz\n170 points possible answered: 2/17\nquestion 3\nfind all solutions to ( 2 cos ( \theta ) =…

chapter 6 quiz\n170 points possible answered: 2/17\nquestion 3\nfind all solutions to ( 2 cos ( \theta ) = sqrt { 2 } ) on the interval ( 0 leq \theta < 2 pi )\n( \theta = )\ngive your answers as exact values, as a list separated by commas.\nadd work\n> next question

chapter 6 quiz\n170 points possible answered: 2/17\nquestion 3\nfind all solutions to ( 2 cos ( \theta ) = sqrt { 2 } ) on the interval ( 0 leq \theta < 2 pi )\n( \theta = )\ngive your answers as exact values, as a list separated by commas.\nadd work\n> next question

Answer

Explanation:

Step1: Solve for (\cos(\theta))

Divide both sides of (2\cos(\theta)=\sqrt{2}) by (2). (\cos(\theta)=\frac{\sqrt{2}}{2})

Step2: Find (\theta) values in ([0, 2\pi))

We know that (\cos(\theta)=\frac{\sqrt{2}}{2}) when (\theta=\frac{\pi}{4}) (in the first - quadrant) and (\theta = 2\pi-\frac{\pi}{4}=\frac{7\pi}{4}) (in the fourth - quadrant) since the cosine function is positive in the first and fourth quadrants.

Answer:

(\frac{\pi}{4},\frac{7\pi}{4})