Summary of Trig functions grade 11 and 12: Horizontal shift

Main Ideas and Concepts

Horizontal Shifting of Trigonometric Graphs:
The video focuses on how trigonometric graphs can shift horizontally, specifically using the sine function as an example. Horizontal shifting is different from vertical shifting and stretching.
Graphing Process:
The speaker demonstrates how to graph the function \( \sin(x) - 30 \) over the interval of 0 to 360 degrees using a calculator. Important steps in using the calculator include:
- Setting the mode to table.
- Inputting the equation.
- Defining the start (0) and end (360) points.
- Setting the step size to \( \frac{\text{Period}}{4} \) (for a sine graph, the period is 360, so the step is 90).
Plotting Points:
The speaker plots key points based on calculator outputs and adjusts for the horizontal shift caused by the \(-30\) in the equation. Important points include:
- At \( x = 0 \), \( y \approx -0.5 \)
- At \( x = 90 \), \( y \approx 0.866 \)
- At \( x = 180 \), \( y \approx -0.5 \)
- At \( x = 270 \), \( y \approx -0.866 \)
- At \( x = 360 \), \( y \approx -0.5 \)
Amplitude, Range, Domain, and Period:
- Amplitude: The maximum distance from the resting position, which is 1 for the sine function.
- Range: The set of y-values, which is from -1 to 1.
- Domain: The set of x-values, which is from 0 to 360 degrees.
- Period: The time it takes for the graph to repeat, which remains 360 degrees for this function since it is only shifted, not stretched or compressed.

Set the calculator to table mode.
Input the equation \( \sin(x) - 30 \).
Define the start point (0) and the end point (360).
Calculate the step size as \( \frac{360}{4} = 90 \).
Plot the points derived from the calculator outputs.
Adjust the plotted points based on the horizontal shift (e.g., \( -30 \) shifts points to the right).
Analyze and label the Amplitude, Range, Domain, and period of the graph.

The speaker in the video is not named, but they are presumably an educator or tutor explaining the concept of horizontal shifting in trigonometric functions.

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