Questions: Find the period of the following equation. y=-1/3 sin (4 pi x+1) Give your answer as a decimal.

Solution Steps

To find the period of the trigonometric function \( y = -\frac{1}{3} \sin (4 \pi x + 1) \), we need to identify the coefficient of \( x \) inside the sine function. The general form of a sine function is \( y = A \sin(Bx + C) \), where the period is given by \( \frac{2\pi}{|B|} \).

In this case, \( B = 4\pi \). Therefore, the period is \( \frac{2\pi}{4\pi} = \frac{1}{2} \).

The given function is \( y = -\frac{1}{3} \sin (4 \pi x + 1) \). The general form of a sine function is \( y = A \sin(Bx + C) \). Here, the coefficient \( B \) is \( 4 \pi \).

The period of a sine function \( y = A \sin(Bx + C) \) is given by \( \frac{2\pi}{|B|} \). Substituting \( B = 4\pi \):

\[ \text{Period} = \frac{2\pi}{|4\pi|} = \frac{2\pi}{4\pi} = \frac{1}{2} \]

Final Answer