Modeling Trigonometric Functions

The video tutorial explains how to model real-world scenarios using trigonometric functions. It covers examples such as a rider's height on a Ferris wheel and ice cream sales, demonstrating how to determine key characteristics like amplitude, vertical translation, period, and phase shift. The tutorial also highlights the flexibility of using sine and cosine functions for modeling periodic data.

What is the primary focus of the video tutorial?

• Modeling trigonometric functions in real-world scenarios

• Understanding quadratic equations

• Modeling linear functions in real-world scenarios

• Exploring polynomial functions

What does the vertical translation of 12 indicate in the Ferris wheel example?

• The rider's starting height above the ground

• The maximum height of the Ferris wheel

• The time taken for one rotation

• The Ferris wheel's diameter

How is the rider's height calculated after 30 seconds?

• By using the cosine function

• By substituting 30 into the height function

• By using the tangent function

• By measuring directly from the ground

What is the period of the Ferris wheel's rotation?

• 90 seconds

• 150 seconds

• 60 seconds

• 120 seconds

Which characteristic is NOT essential for modeling trigonometric functions?

• Amplitude

• Phase shift

• Vertical translation

• Color of the graph

What is the amplitude of the ice cream sales model?

• 45

• 176

• 199

• 380

How can periodic data be modeled using trigonometric functions?

• With linear functions

• Only with sine functions

• Only with cosine functions

• With both sine and cosine functions

What is the phase shift in the second Ferris wheel example?

• 5 units to the left

• 10 units to the right

• 5 units to the right

• 10 units to the left

What is the passenger's height at 78 seconds?

• 11 meters

• 1 meter

• 8.98 meters

• 6 meters