Study guides › Level 9 · Trigonometry

Amplitude and period of a sine wave

Level 9 · Trigonometry · for questions like “What is the period of y = 3 sin(2x)?”

💡 The idea

For y = a sin(bx) or y = a cos(bx):

• amplitude = |a|: how high the wave goes above the middle.
• period = 2π ÷ b: how long one full wave takes.

✏️ Worked examples

1. y = 3 sin(2x): amplitude 3, period 2π ÷ 2 = π.

2. y = −5 cos(4x): amplitude 5 (ignore the minus sign), period π/2.

⚠️ Watch out

• The number in front doesn't change the period.
• A bigger b squeezes the waves closer, so the period gets shorter.

🎯 Try these

1. Amplitude of y = 4 sin(3x)
2. Period of y = 2 cos(3x)
3. Period of y = sin(6x)

Answers: 1) 4 2) 2π/3 3) π/3

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