7) \( \cos \left(2 x+\frac{\pi}{6}\right)=-\frac{\pi}{3} \)
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Bonus Knowledge
First things first, we've got a little mix-up here! The equation \( \cos \left(2x+\frac{\pi}{6}\right) = -\frac{\pi}{3} \) is not quite correct, as the cosine function only outputs values in the range of -1 to 1. Therefore, -\(\frac{\pi}{3}\) (approximately -1.05) is not a valid output for the cosine function, making this equation impossible to satisfy. When dealing with misunderstandings in trigonometry or even in math in general, it’s crucial to remember the basic constraints of the functions you’re working with. Always keep in check the values that your trigonometric functions can yield; things can get dicey if you venture outside those bounds!
