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OLga [1]
2 years ago
11

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.
Mathematics
1 answer:
lana66690 [7]2 years ago
6 0
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
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