Explanation:
In trigonometry, the function \( \cos(\theta + 90^\circ) \) is equivalent to \( -\sin(\theta) \).
The cosine function represents the x-coordinate of a point on the unit circle corresponding to an angle \( \theta \), while the sine function represents the y-coordinate.
When we shift the angle by \( 90^\circ \) (or \( \frac{\pi}{2} \) radians), we are essentially moving counterclockwise on the unit circle. This means that the cosine function will reach its peak at \( \theta = 0^\circ \) and then start to decrease, while the sine function will reach its peak at \( \theta = 90^\circ \) and then start to decrease.
So, \( \cos(\theta) \) leads \( \cos(\theta + 90^\circ) \), or equivalently, \( \cos(\theta) \) leads \( -\sin(\theta) \).