Trigonometric Modeling and Tide Analysis

Anil Kumar explains how to model real-life situations using trigonometric functions, focusing on the example of water depth in a harbor. The video covers deriving both cosine and sine functions to represent the tidal changes, including calculating amplitude, phase shift, and period. Graphical representation and problem-solving techniques are also discussed, providing a comprehensive understanding of the application of trigonometric functions in real-world scenarios.

What is the main focus of the video tutorial?

• Understanding calculus concepts

• Modeling real-life situations with trigonometric functions

• Learning about geometry

• Exploring algebraic equations

What is the maximum water depth mentioned in the problem?

• 10 meters

• 12 meters

• 15 meters

• 20 meters

How often is one cycle of the tide completed?

• Every 6 hours

• Every 8 hours

• Every 10 hours

• Every 12 hours

What is the minimum water depth in the harbor?

• 5 meters

• 7 meters

• 9 meters

• 11 meters

At what time does the high tide occur?

• 9 hours

• 8 hours

• 7 hours

• 6 hours

What is the amplitude of the cosine function derived?

• 5

• 3

• 4

• 2

What is the average value of the water depth?

• 12

• 11

• 10

• 9

What is the value of K in the cosine function?

• 30

• 25

• 20

• 15

What is the phase shift for the cosine function?

• 5

• 7

• 6

• 8

What is the equation of the cosine function derived?

• y = 4 * COS(30 * (x - 8)) + 11

• y = 5 * COS(35 * (x - 9)) + 12

• y = 3 * COS(25 * (x - 7)) + 10

• y = 6 * COS(40 * (x - 10)) + 13