The functions f(θ) and g(θ) are sine functions, where f(0)=g(0)=0 . The amplitude of f(θ) is twice the amplitude of g(θ) . The period of f(θ) is one-half the period of g(θ) . If g(θ) has a period of 2π and f(π4)=4 , write the function rule for g(θ) . Explain your reasoning in short term

Answer 1

Given that g(θ) has a period of 2π and the amplitude is half that of f(θ), we can determine the function rule for g(θ) as follows:

Since g(0) = 0 and g(2π) = 0 (since the period is 2π), g(θ) can be represented as: g(θ) = sin(θ)

Now, since the amplitude of g(θ) is half that of f(θ), we know that the amplitude of g(θ) is 2.

So the function rule for g(θ) is: g(θ) = 2sin(θ)

This function rule satisfies the conditions given and reflects the properties of g(θ) outlined above.