Final Answer:
If (y = cos(x)) equals zero at π/2, then (y = -cos(x)) equals zero at (frac{3π}{2}).
Step-by-step explanation:
The cosine function, (y = cos(x)), equals zero at points where (x) is an odd multiple of (frac{π}{2}) in the unit circle. Specifically, (y = cos(frac{π}{2})) is zero, and this occurs at (frac{π}{2}). To find when (y = -cos(x)) equals zero, we look for points where the cosine function is equal to zero. Since the cosine function is an even function (\(cos(-x) = cos(x)\)), the points where \(y = -cos(x)) equals zero are at the opposite locations to those of \(y = cos(x)\) in the unit circle. Therefore, \(y = -cos(\frac{π}{2})\) is zero, and this occurs at (frac{3π}{2\).
In summary, if \(y = cos(x)\) equals zero at (frac{π}{2}), then (y = -cos(x)) equals zero at (frac{3π}{2}). This relationship stems from the properties of the cosine function and the symmetry of the unit circle.