4e definitions (Basics of Graphing Sine, Cosine, Tangent)

The video tutorial explores the trigonometric graphs of sine, cosine, and tangent, focusing on their transformations and characteristics. It explains how transformations using parameters A, B, C, and D affect these graphs, including vertical and horizontal stretches, compressions, and shifts. The tutorial also covers the periodic nature of these graphs, detailing the initial periods and how to determine the start and end points. Special attention is given to the tangent graph's unique properties, such as its asymptotes and different period compared to sine and cosine.

What does the parameter 'A' affect in a trigonometric function?

• Horizontal shift

• Vertical stretch or compression

• Phase shift

• Frequency

How does a negative 'A' value affect the sine graph?

• It shifts the graph to the right

• It reflects the graph over the X-axis

• It stretches the graph horizontally

• It compresses the graph vertically

What is the effect of increasing the 'B' value in a sine function?

• Increases the amplitude

• Shifts the graph vertically

• Decreases the frequency

• Increases the frequency

What is the initial period of the sine function?

• 2π

• π

• π/2

• 3π

How do you determine the phase shift of a trigonometric function?

• By solving Bθ - C = 0

• By analyzing the amplitude

• By calculating 2π/B

• By finding the vertical shift

What is the range of a sine function with an amplitude of 3?

• [-1, 1]

• [-3, 3]

• [0, 3]

• [-2, 2]

What is the period of a tangent function?

• 3π

• π/2

• 2π

• π

Where do the asymptotes of the tangent function occur?

• At every π/2

• At every 2π

• At every 3π/2

• At every π

How do you find the new starting point of a tangent function?

• Set Bθ - C = 2π

• Set Bθ - C = π/2

• Set Bθ - C = π

• Set Bθ - C = 0

What is the domain of the tangent function?

• All real numbers except where tan(x) = 0

• All real numbers except where cos(x) = 0

• All real numbers except where sin(x) = 0

• All real numbers