**Graph \[y=5\sin\left(\dfrac{\pi}{2}x\right)-4\] in the interactive widget.***.*

\[\small{1}\]\[\small{2}\]\[\small{3}\]\[\small{4}\]\[\small{5}\]\[\small{6}\]\[\small{7}\]\[\small{8}\]\[\small{9}\]\[\small{\llap{-}2}\]\[\small{\llap{-}3}\]\[\small{\llap{-}4}\]\[\small{\llap{-}5}\]\[\small{\llap{-}6}\]\[\small{\llap{-}7}\]\[\small{\llap{-}8}\]\[\small{\llap{-}9}\]\[\small{1}\]\[\small{2}\]\[\small{3}\]\[\small{4}\]\[\small{5}\]\[\small{6}\]\[\small{7}\]\[\small{8}\]\[\small{9}\]\[\small{\llap{-}2}\]\[\small{\llap{-}3}\]\[\small{\llap{-}4}\]\[\small{\llap{-}5}\]\[\small{\llap{-}6}\]\[\small{\llap{-}7}\]\[\small{\llap{-}8}\]\[\small{\llap{-}9}\]\[y\]\[x\]

Here is the graph of the function \( y = 5\sin\left(\dfrac{\pi}{2}x\right) - 4 \). You can observe that it represents a sine wave with an amplitude of 5, shifted vertically by -4, and the argument scaled horizontally by \( \frac{\pi}{2} \).

Would you like further details or explanations on any aspect of this graph?

Here are 5 related questions for deeper exploration:
1. How does the amplitude of a sine function affect its graph?
2. What is the effect of a vertical shift on the sine graph?
3. How does the frequency change when modifying the argument of the sine function?
4. What are the periodic properties of this sine function?
5. How would the graph change if the coefficient of sine was negative?

**Tip:** The period of a sine function \( y = a \sin(bx + c) + d \) is determined by \( \frac{2\pi}{|b|} \).

Graph y = 5sin(π/2 x) - 4 in the interactive widget.

Explore the graph of y = 5sin(π/2 x) - 4, a sine function with an amplitude of 5 and a vertical shift of -4. Learn about the effects of amplitude, frequency, and shifts in trigonometric graphs. Suitable for high school students in Grades 10-12.

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