Transformations of Trigonometric Functions

This tutorial covers sketching trigonometric graphs, focusing on transforming the standard sine and cosine graphs. It explains how to sketch y = sin(2x - 30) by transforming y = sin x and y = cos(3x + 45) by transforming y = cos x. The tutorial discusses transformations like stretching and translating graphs along the x-axis.

What is the main focus of this tutorial?

• Sketching the graph of y = sin(2x - 30)

• Solving trigonometric equations

• Understanding the unit circle

• Learning about trigonometric identities

What is the range of the standard sine function y = sin(x)?

• 0 to 1

• -1 to 1

• -2 to 2

• -1 to 0

At which degrees does the sine function y = sin(x) cross the x-axis?

• 0°, 90°, 180°

• 90°, 270°, 360°

• 0°, 180°, 360°

• 90°, 180°, 270°

What is the amplitude of the standard sine function y = sin(x)?

• 0

• 2

• 1

• 3

What is the period of the standard sine function y = sin(x)?

• 360°

• 180°

• 90°

• 270°

What is the initial value of y = sin(x) at x = 0?

• 0

• 1

• -1

• 0.5

What is the maximum value of y = sin(x)?

• 0

• 1

• -1

• 2

What transformation occurs when changing from y = sin(x) to y = sin(2x)?

• Vertical translation

• Horizontal stretch

• Horizontal translation

• Vertical stretch

How does the graph of y = sin(2x) differ from y = sin(x)?

• It is shifted upwards

• It is compressed horizontally

• It is shifted downwards

• It is stretched vertically

What is the frequency of the function y = sin(2x)?

• 1

• 2

• 4

• 3