What is the effect of increasing the amplitude of a sine or cosine function?

What is the effect of increasing the amplitude of a sine or cosine function?

• A. It changes the period
• B. It increases vertical stretch, height of peaks and troughs
• C. It shifts the midline
• D. It shifts left or right

Answer: (B)

Increasing the amplitude makes the graph stretch vertically, so the peaks get higher and the troughs get lower. The midline stays where it is, and the distance between the midline and a peak or trough grows with larger amplitude. The period, which is how long it takes to repeat, isn’t affected by amplitude—it depends on the horizontal scaling (how the x-values are stretched or compressed). So, you can picture it as the wave becoming taller without changing how wide each cycle is or where the wave sits vertically unless you adjust a separate vertical shift. For example, going from y = sin x to y = 2 sin x doubles the height of the peaks and depths of the troughs while leaving the midline at 0 and the period the same.

Increasing the amplitude makes the graph stretch vertically, so the peaks get higher and the troughs get lower. The midline stays where it is, and the distance between the midline and a peak or trough grows with larger amplitude. The period, which is how long it takes to repeat, isn’t affected by amplitude—it depends on the horizontal scaling (how the x-values are stretched or compressed). So, you can picture it as the wave becoming taller without changing how wide each cycle is or where the wave sits vertically unless you adjust a separate vertical shift. For example, going from y = sin x to y = 2 sin x doubles the height of the peaks and depths of the troughs while leaving the midline at 0 and the period the same.