How to Graph the Sine Graph with Period Change

The video tutorial explains how to graph the function F(x) = sin(x/3). It covers the standard form of trigonometric graphs, focusing on the importance of amplitude and period. The tutorial details how to calculate the period and identify critical points, such as maximum, minimum, and x-intercepts. It also discusses the absence of phase shifts and vertical translations in this specific function. Finally, the video demonstrates graphing the sine function, highlighting the critical points and the behavior of the graph over two full periods.

What is the standard form of a trigonometric function used in graphing?

• a * sin(bx - c) + d

• a * cos(bx) + c

• a * tan(bx) - d

• a * cot(bx + c)

How is the amplitude of the function F(x) = sin(x/3) determined?

• By the value of b

• By the phase shift

• By the absolute value of a

• By the coefficient of x

What is the period of the function F(x) = sin(x/3)?

• 2π

• 6π

• π/3

• 3π

How do you find the critical points of a sine function?

• By adding the phase shift

• By dividing the period by 2

• By multiplying the amplitude by 4

• By dividing the period by 4

What is the significance of a phase shift in graphing?

• It shifts the graph left or right

• It affects the vertical translation

• It changes the amplitude

• It alters the period

What is the first critical point of the function F(x) = sin(x/3)?

• 0

• 6π

• 3π/2

• π

How does the sine function behave at its critical points?

• It only increases

• It remains constant

• It only decreases

• It reaches maximum and minimum values