Question

What is the general equation of a sine function with an amplitude of 2, a period of pi and a horizontal shift of pi units?

Answer 1

Answer:

The general form of the sine function is $y=2\sin(2(x-\pi))$

Explanation:

The general form of a sinusoidal function is in the form

$y=A\sin(B(x-C))+D$

Here, A = amplitude

C = Horizontal shift

D = Vertical shift or mid line

The formula for finding the period is $P=\frac{2\pi}{B}$

Further Explanation:

It has been given that, the amplitude is 2. Thus, A = 2

Now, the period is π. Thus, we can use the formula for period for finding the value of B.

$P=\frac{2\pi}{B}\\\\\pi=\frac{2\pi}{B}\\\\B=2$

Therefore, the value of B is 2.

Now, since the variable c is phase shift or horizontal shift and it has been given that horizontal shift is π units.

Thus, C = π

Therefore, the general form of the sine function is

$y=2\sin(2(x-\pi))$

Learn More:

brainly.com/question/5470844 (Answered by Eudora)

brainly.com/question/7280065 (Answered by Merlynthewhizz)

Keywords:

• general form  sinusoidal functions
• Sinusoidal graphs

• Amplitude and period of sinusoidal functions

Answer 2

Y= (amplitude).sin(2π/period).(x-shift)

= 2.sin(2π/π)(x-π)


=2.sin[2.(x-π)]