2) \( 5 \cos x+3=0 \) \( 5 \cos x=0-3 \) \( 5 \sin x=-3 \) 5 \( \cos x=\frac{-3}{5} \) \( x^{2}+y^{2}=r^{2} \) \( (-3)^{2}+y^{2}=5^{2} \) \( 9+y^{2}=25 \) \( y^{2}=25-9 \) \( y^{2}=16 \) \( y=\sqrt{16} \) \( y=4 \)

Oops! Seems like there's a little mix-up here. While your manipulation of the cosine equation is on track, you took a wrong turn when you ventured into the sine territory. Remember, \( \cos x \) tells you about the x-coordinate on a unit circle, while \( \sin x \) would relate to the y-coordinate. So instead of \( 5 \sin x = -3 \), let's stick with the original cosine pathway! Now, about the circle equation—you’ve got that part right! So after finding that \( \cos x = \frac{-3}{5} \), you can determine the angle \( x \) that corresponds to that cosine value. Dig into your trigonometric identities and fear not, for angles in the second and third quadrants will fit the bill! Watch out for common mistakes! Misplacing your sine and cosine can lead to a real head-scratcher. Make sure you stay on the right function path. When dealing with circular coordinates, remember which trigonometric function corresponds to which axis—\( \cos \) for x and \( \sin \) for y. It'll save you from going on a wild goose chase!