Trigonometric Functions and Their Properties

This video tutorial introduces trig transformations, focusing on the function y = -3 cosine 6x. It explains how the values of A and B affect amplitude and period, respectively. The amplitude is the absolute value of A, and the period is calculated as 2PI divided by B. The video demonstrates graphing the function over one period, highlighting the reflection across the X-axis due to the negative A value. It provides a step-by-step guide to dividing the interval into equal parts and sketching the graph. The tutorial concludes with notes on transformations of sine and cosine functions.

What is the value of A in the function Y = -3 cosine 6X?

• 6

• 3

• -6

• -3

How does a negative A value affect the graph of a trig function?

• It shifts the graph downwards.

• It stretches the graph vertically.

• It reflects the graph across the X-axis.

• It shifts the graph upwards.

What is the formula to calculate the period of a trig function?

• 2PI divided by A

• 2PI divided by B

• 2PI multiplied by B

• PI divided by B

What is the period of the function Y = -3 cosine 6X?

• PI/3

• PI/6

• 2PI/3

• PI

When graphing the function, into how many parts should the interval be divided?

• Five equal parts

• Two equal parts

• Three equal parts

• Four equal parts

What is the maximum value of the function Y = -3 cosine 6X?

• -6

• 6

• -3

• 3

What is the minimum value of the function Y = -3 cosine 6X?

• 3

• -3

• 6

• -6

In the graph of the function Y = -3 cosine 6X, where does the graph start?

• At a maximum of 3

• At a minimum of -3

• At the midline

• At a maximum of 6

What is the next point after the starting point in the graph of Y = -3 cosine 6X?

• At a maximum

• At a maximum of 6

• At a minimum

• At the midline

What should be done if a larger interval of the graph is needed?

• Reflect the graph again

• Change the value of B

• Extend the graph using the same pattern

• Recalculate the amplitude