How many solutions exist for the equation 3Cos 2x=-3 in the interval 0<=x<=2Pi The 2 confuses me. How do I adjust for that? Thanks

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- Oct 23rd 2008, 02:52 PMIDontunderstandTrig equations
How many solutions exist for the equation 3Cos 2x=-3 in the interval 0<=x<=2Pi The 2 confuses me. How do I adjust for that? Thanks

- Oct 23rd 2008, 03:14 PMskeeter
$\displaystyle 3\cos(2x) = -3$

$\displaystyle \cos(2x) = -1$

since $\displaystyle 0 \leq x \leq 2\pi$ , then $\displaystyle 0 \leq 2x \leq 4\pi$

$\displaystyle 2x = \pi$

$\displaystyle x = \frac{\pi}{2}$

$\displaystyle 2x = 3\pi$

$\displaystyle x = \frac{3\pi}{2}$