1. **State the problem:** We want to write an equation equivalent to $y = -6\cos\left(x + \frac{\pi}{2}\right) + 4$ using the sine function. 2. **Recall the trigonometric identity:** $\cos\left(x + \frac{\pi}{2}\right) = -\sin x$. 3. **Apply the identity:** Substitute $\cos\left(x + \frac{\pi}{2}\right)$ with $-\sin x$ in the original equation: $$y = -6 \times \left(-\sin x\right) + 4$$ 4. **Simplify:** $$y = 6 \sin x + 4$$ 5. **Final answer:** The equivalent equation using the sine function is: $$y = 6 \sin x + 4$$