write the equation of a sine function with amplitude = 2 and period = π. type the equation in the form y = a…

write the equation of a sine function with amplitude = 2 and period = π. type the equation in the form y = a sin(ωx) or y = a cos(ωx) with ω > 0. select the correct choice and, if necessary, fill in the answer box(es) to complete your choice. a. there are two equations; the equation when a < 0 is y = □ and the equation when a > 0 is y = □. (simplify your answers. type exact answers, using π as needed. use integers or fractions for any numbers in the expressions.) b. there is one equation. it is y = □. (simplify your answer. type an exact answer, using π as needed. use integers or fractions for any numbers in the expression.) c. there are no equations with these characteristics.

write the equation of a sine function with amplitude = 2 and period = π. type the equation in the form y = a sin(ωx) or y = a cos(ωx) with ω > 0. select the correct choice and, if necessary, fill in the answer box(es) to complete your choice. a. there are two equations; the equation when a < 0 is y = □ and the equation when a > 0 is y = □. (simplify your answers. type exact answers, using π as needed. use integers or fractions for any numbers in the expressions.) b. there is one equation. it is y = □. (simplify your answer. type an exact answer, using π as needed. use integers or fractions for any numbers in the expression.) c. there are no equations with these characteristics.

Answer

Explanation:

Step1: Recall the formula for amplitude and period

The general form of a sine function is (y = A\sin(\omega x)) or (y=A\cos(\omega x)). The amplitude is (|A|) and the period (T=\frac{2\pi}{\omega}). Given that the amplitude (|A| = 2), so (A=\pm2). Given that the period (T = \pi).

Step2: Solve for (\omega)

Since (T=\frac{2\pi}{\omega}) and (T = \pi), we substitute (T) into the formula: (\pi=\frac{2\pi}{\omega}). Cross - multiply gives (\pi\omega=2\pi). Divide both sides by (\pi) (since (\pi\neq0)), we get (\omega = 2).

Answer:

A. There are two equations; the equation when (A<0) is (y=- 2\sin(2x)) (or (y = - 2\cos(2x))) and the equation when (A>0) is (y = 2\sin(2x)) (or (y=2\cos(2x)))