Sine Function Concepts and Applications

This video tutorial explains how to describe and graph a trigonometric transformation, specifically focusing on the function y = 1/2 sine (x + pi/4). It covers identifying the amplitude and phase shift, understanding the direction of the phase shift, and graphing the function by dividing the interval into equal parts. The tutorial concludes with a review of how parameters affect the graph of sine and cosine functions.

What is the value of 'A' in the function Y = 1/2 SINE (X + PI/4)?

• -PI/4

• PI/4

• 1/2

• 1

How does the value of 'A' affect the sine function?

• It changes the period

• It changes the vertical shift

• It changes the phase shift

• It changes the amplitude

What is the phase shift of the function Y = 1/2 SINE (X + PI/4)?

• PI/4 to the left

• PI/4 to the right

• 2PI to the left

• No shift

In which direction is the phase shift if D = -PI/4?

• To the left

• To the right

• Upwards

• No shift

What is the period of the basic sine function?

• 3PI

• PI

• 2PI

• PI/2

How is the interval for graphing adjusted due to the phase shift?

• From -2PI to 2PI

• From PI/4 to 2PI

• From -PI/4 to 7PI/4

• From 0 to 2PI

What is the maximum value of the function Y = 1/2 SINE (X + PI/4)?

• 0

• -1/2

• 1/2

• 1

Where does the sine function start when plotting with a phase shift of -PI/4?

• At PI/4

• At 2PI

• At -PI/4

• At 0

What is the pattern of the sine function when plotting?

• Starts at minimum, then midline, then maximum

• Starts at midline, then minimum, then maximum

• Starts at midline, then maximum, then midline

• Starts at maximum, then midline, then minimum

What should you review to understand how A, B, C, and D affect sine and cosine graphs?

• The Pythagorean theorem

• The basic sine function

• The unit circle

• The notes on transformations