Graph Transformations and Sketching Techniques

The video tutorial by Avenel Kuma explains how to sketch the graph of the trigonometric function y = 2sin(-2θ + 60°) for θ between 0° and 180°. The process involves transforming the equation, understanding the effects of negative angles, and applying graphing techniques. The tutorial covers reflection on the x-axis, horizontal compression, phase shift, and amplitude. It provides a step-by-step guide to sketching the graph in two phases, with detailed explanations of each transformation and adjustment.

What is the initial step in rewriting the equation y = 2sin(-2θ + 60°)?

• Subtract 60 degrees from the angle

• Multiply the entire equation by 2

• Add 30 degrees to the angle

• Factor out -2 from the angle

Which transformation is NOT involved in the function y = 2sin(-2θ + 60°)?

• Reflection on the x-axis

• Vertical stretch

• Phase shift

• Horizontal compression

What is the new time period of the sine wave after applying the transformations?

• 270 degrees

• 90 degrees

• 180 degrees

• 360 degrees

In the approach to sketch the graph, what is the first step?

• Reflect the graph on the y-axis

• Sketch the graph with phase shift

• Sketch the graph without phase shift

• Apply vertical translation

How is the graph divided to facilitate sketching?

• Into two halves

• Into five segments

• Into four quarters

• Into three halves

What is the purpose of dividing the graph into quarters?

• To change the time period

• To apply vertical translation

• To simplify the phase shift

• To adjust the amplitude

What is the phase shift applied to the graph?

• 30 degrees to the left

• 60 degrees to the left

• 60 degrees to the right

• 30 degrees to the right

What is the final step in sketching the graph?

• Reflect the graph on the y-axis

• Join the points to complete the graph

• Apply a vertical stretch

• Add a horizontal translation

What alternative method is mentioned for sketching the graph?

• Using a vertical reflection

• Sketching on the left side of the curve

• Applying a different phase shift

• Changing the amplitude

What is the final range of the graph after all transformations?

• 30 to 180 degrees

• 0 to 360 degrees

• 30 to 210 degrees

• 0 to 180 degrees