Some one gets on to a ferris wheel 30^0 left of the bottom. What would be the phase shift if I am writing a sine Function?
Is it -120^0 or + 120^0. Please explain.
is the wheel rising or falling from that point?
Some one gets on to a ferris wheel 30^0 left of the bottom. What would be the phase shift if I am writing a sine Function?
Is it -120^0 or + 120^0. Please explain.
It's turning counter clockwise.
so, it will achieve its minimum height when θ=30
sinθ achieves its minimum height when θ=270
sin(30+240) = sin(30-120)
the graph shows this.
http://www.wolframalpha.com/input/?i=sin(x-2pi%2F3)
To determine the phase shift for the given situation, we need to first understand what phase shift represents in a sinusoidal function.
In a sine function, the phase shift represents the horizontal displacement or the horizontal shift of the graph. It indicates how much the graph is shifted left or right from the usual starting position.
In this case, the person gets on the Ferris wheel 30 degrees to the left of the bottom. Since the complete rotation of a circle is 360 degrees, we can divide it into four quadrants (0 degrees to 90 degrees, 90 degrees to 180 degrees, 180 degrees to 270 degrees, and 270 degrees to 360 degrees).
Given that the person gets on to the Ferris wheel 30 degrees to the left of the bottom, it means that they start their ride in the third quadrant (180 degrees to 270 degrees). However, we usually measure angles in a counterclockwise direction, so we need to convert this angle to a positive value.
To find the phase shift, we need to consider the position of the starting point of the graph of the sine function. The usual starting position of a sine function is at 0 degrees, which is the rightmost point on the x-axis.
Therefore, if the person gets on the Ferris wheel 30 degrees to the left of the bottom, we can calculate the phase shift as follows:
Phase shift = 360 degrees - 180 degrees + 30 degrees
Phase shift = 210 degrees + 30 degrees
Phase shift = 240 degrees
So, in this case, the phase shift for a sine function representing the person's ride on the Ferris wheel would be +240 degrees.