Transformations of Sine and Cosine Functions

The video tutorial covers transformations of trigonometric functions, focusing on horizontal and vertical shifts. It explains how to graph sinusoidal functions with these transformations and analyzes the effects on the graph. The tutorial also explores transformations of the cosine function, providing visual cues and examples to aid understanding.

What is the next logical transformation after vertical shift?

• Vertical reflection

• Horizontal shift

• Horizontal stretch

• Vertical stretch

When shifting the sine curve horizontally, what happens to the range?

• It increases

• It decreases

• It remains the same

• It becomes undefined

How many degrees faster does the sine curve reach 180° after a 30° left shift?

• 90°

• 60°

• 120°

• 30°

What is the new turning point of the sine curve after a 30° left shift?

• 60°

• 120°

• 90°

• 150°

What part of the sine graph is missing after a 30° left shift?

• No part is missing

• The last 30°

• The first 30°

• The middle 30°

After shifting the sine graph, where does the missing part reappear?

• It does not reappear

• At the beginning

• At the end

• In the middle

What is the effect of a 180° right shift on the cosine graph?

• It stretches vertically

• It moves to the left

• It moves to the right

• It compresses horizontally

How does the cosine graph compare to the sine graph after a horizontal shift?

• They have opposite transformations

• They have similar transformations

• They are mirror images

• They are identical

What happens to the midpoint of the cosine graph after a 180° shift?

• It remains unchanged

• It moves to 0°

• It moves to 180°

• It moves to 360°

What is a helpful visual cue when drawing the cosine graph?

• Using a calculator

• Drawing a small cosine graph

• Using a ruler

• Drawing a sine graph first