The function f (theta) and g (theta) are sine functions where f (0) = g (0) = 0. The amplitude of f (theta) is twice the amplitude of g (theta). The period of f (theta) is one-half the period of g (theta). If g (theta) has a period of 2x, and f (pi/4) = 4, write the function rule for g (theta). Explain your reasoning.

Question

Mathematics

Isabel Berry

31 December, 01:08

The function f (theta) and g (theta) are sine functions where f (0) = g (0) = 0. The amplitude of f (theta) is twice the amplitude of g (theta). The period of f (theta) is one-half the period of g (theta). If g (theta) has a period of 2x, and f (pi/4) = 4, write the function rule for g (theta). Explain your reasoning.

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Answers (1)

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Tia Warner · Answer 1

Because the values of both functions is 0 at ∅ = 0, both have an equilibrium position of 0.

Next, we can use the given value of f (∅) to find the amplitude:

4 = Asin (π/4)

4 = A (√2 / 2)

A = 8 / √2

We halve this amplitude to find the amplitude of g (∅):

A = 4 / √2

The period is 2π/2 = π

g (∅) = 4sin (∅/2) / √2