find the period of the function and use the language of transformations to describe how the graph of the…

find the period of the function and use the language of transformations to describe how the graph of the function is related to the graph of y = sin x. y = 6 sin 5x what is the period of the function? (simplify your answer. use integers or fractions for any numbers in the expression. type an exact answer, using π as needed.) how is the graph of the function related to the graph of y = sin x? choose the correct answer below. a. the graph of y = 6 sin 5x is a horizontal shrink of the graph of y = sin x by a factor of 1/6 and a vertical stretch by a factor of 5. b. the graph of y = 6 sin 5x is a horizontal stretch of the graph of y = sin x by a factor of 5 and a vertical stretch by a factor of 6. c. the graph of y = 6 sin 5x is a horizontal stretch of the graph of y = sin x by a factor of 6 and a vertical stretch by a factor of 5. d. the graph of y = 6 sin 5x is a horizontal shrink of the graph of y = sin x by a factor of 1/5 and a vertical stretch by a factor of 6. w an example get more help -

find the period of the function and use the language of transformations to describe how the graph of the function is related to the graph of y = sin x. y = 6 sin 5x what is the period of the function? (simplify your answer. use integers or fractions for any numbers in the expression. type an exact answer, using π as needed.) how is the graph of the function related to the graph of y = sin x? choose the correct answer below. a. the graph of y = 6 sin 5x is a horizontal shrink of the graph of y = sin x by a factor of 1/6 and a vertical stretch by a factor of 5. b. the graph of y = 6 sin 5x is a horizontal stretch of the graph of y = sin x by a factor of 5 and a vertical stretch by a factor of 6. c. the graph of y = 6 sin 5x is a horizontal stretch of the graph of y = sin x by a factor of 6 and a vertical stretch by a factor of 5. d. the graph of y = 6 sin 5x is a horizontal shrink of the graph of y = sin x by a factor of 1/5 and a vertical stretch by a factor of 6. w an example get more help -

Answer

Explanation:

Step1: Recall period - formula for sine function

The general form of a sine - function is $y = A\sin(Bx - C)+D$, and its period is given by $T=\frac{2\pi}{|B|}$. For the function $y = 6\sin(5x)$, $B = 5$. $T=\frac{2\pi}{5}$

Step2: Analyze horizontal and vertical transformations

For the function $y = A\sin(Bx)$ compared to $y=\sin(x)$:

  • The horizontal transformation: If $y=\sin(x)$ is transformed to $y=\sin(Bx)$, when $B>1$, it is a horizontal shrink. Here $B = 5$, so the graph of $y=\sin(x)$ is horizontally shrunk by a factor of $\frac{1}{5}$.
  • The vertical transformation: If $y=\sin(x)$ is transformed to $y = A\sin(x)$, when $A>1$, it is a vertical stretch. Here $A = 6$, so the graph of $y=\sin(x)$ is vertically stretched by a factor of 6.

Answer:

The period of the function is $\frac{2\pi}{5}$. D. The graph of $y = 6\sin(5x)$ is a horizontal shrink of the graph of $y=\sin(x)$ by a factor of $\frac{1}{5}$ and a vertical stretch by a factor of 6.