Question

For each function, give the amplitude, period, vertical translation, and phase shift, as applicable.y = 2 - sin(3x - π/5)

Accepted Answer

Identify the general form of the sine function: $$y = A \sin(Bx - C) + D$$, where $$A is $$the amplitude, $$\frac{2\pi}{B} is $$the period, $$D is $$the vertical translation, and the phase shift is given by $$\frac{C}{B}. $$Rewrite the given function $$y = 2 - \sin(3x - \frac{\pi}{5}) to $$match the general form. Notice that $$2 - \sin(3x - \frac{\pi}{5})$$ can be seen as $$y = -\sin(3x - \frac{\pi}{5}) + 2. $$Determine the amplitude $$A by $$taking the absolute value of the coefficient in front of the sine function. Here, the coefficient is $$-1$$, so $$A = | -1 | = 1. $$Calculate the period using the formula $$	ext{Period} = \frac{2\pi}{B}$$, where $$B is $$the coefficient of $$x$$ inside the sine function. Here, $$B = 3$$, so the period is $$\frac{2\pi}{3}. $$Find the vertical translation $$D$$, which is the constant added outside the sine function. Here, $$D = 2. $$Then, find the phase shift by dividing $$C by$$ $$B$$: $$	ext{Phase shift} = \frac{\frac{\pi}{5}}{3} = \frac{\pi}{15}. $$Since the function is $$\sin(3x - \frac{\pi}{5})$$, the phase shift is to the right by $$\frac{\pi}{15}.$$

For each function, give the amplitude, period, vertical translation, and phase shift, as applicable.
y = 2 - sin(3x - π/5)

비슷한 문제에 대한 검증된 영상 답변:

주요 개념

Amplitude of a Trigonometric Function

Period of a Sine Function

Vertical Translation and Phase Shift