What are the periods?

Question

directions: find the period and amplitude

ok so i know the amplitudes but i'm unsure about the periods.

1. y = 2 cos 3x

2. y = 5 sin 0.5x

3. y = cos pi(x)

Answer 1

y = acos(bx)

y = asin(bx)

Amplitude = a

Period = 2π/b, for both cosine and sine functions (π/b for tangent)

Thus,

1. period = 2π/3, a = 2

2. period = 2π/0.5 = 4π, a = 5

3. period = 2π/π = 2, a = 1

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