Trigonometric Transformations and Graphs: Finding Periods and Defining Symmetries

The video tutorial delves into trigonometric transformations, focusing on the periodic nature of sine, cosine, and tangent graphs. It explains how to find the period of these graphs and demonstrates transformations using examples. The tutorial also explores the symmetries in trigonometric graphs, providing insights into how transformations affect their appearance.

What is the period of the sine function?

• 270 degrees

• 90 degrees

• 360 degrees

• 180 degrees

What is the period of the tangent function?

• 180 degrees

• 360 degrees

• 270 degrees

• 90 degrees

Which transformation is applied first when transforming a graph?

• Vertical stretch

• Horizontal stretch

• Horizontal translation

• Vertical translation

In the transformation y = 3 sin(x - 45), what does the '3' represent?

• Horizontal translation

• Vertical translation

• Vertical stretch

• Horizontal stretch

In the transformation y = tan(-2x) + 1/2, what does the '+ 1/2' represent?

• Horizontal translation

• Vertical stretch

• Vertical translation

• Horizontal stretch

How does a negative sign in front of the x in a trigonometric function affect the graph?

• Reflects in the x-axis

• Reflects in the y-axis

• Stretches vertically

• Stretches horizontally

Which trigonometric function remains unchanged when reflected in the y-axis?

• Sine

• Cosine

• Tangent

• Secant