Trigonometric Functions and Their Properties

This video tutorial demonstrates how to graph the trigonometric functions cosine, sine, and tangent over a specified interval using Desmos. It covers the key characteristics of each function, including their periods, maximum and minimum values, and patterns. The tutorial also provides guidance on graphing these functions by hand, focusing on one period and breaking it into subintervals to recognize patterns. The tangent function's unique properties, such as its undefined points and vertical asymptotes, are also discussed.

What is the first step in graphing functions using Desmos?

• Draw the graph manually.

• Enter the function equation in the graphing calculator.

• Adjust the y-axis range.

• Change the calculator to degree mode.

What is the period of the basic cosine function?

• 4 Pi radians

• Pi radians

• 2 Pi radians

• 3 Pi radians

How is the cosine function pattern described over one period?

• Min, midline, max, midline

• Max, midline, min, midline, max

• Midline, max, midline, min

• Max, min, max, min

What is the maximum value of the sine function?

• -1

• 1

• 2

• 0

How does the pattern of the sine function differ from the cosine function?

• It starts at zero.

• It starts at the midline.

• It starts at a minimum.

• It starts at a maximum.

What is the period of the tangent function?

• 3 Pi radians

• 4 Pi radians

• 2 Pi radians

• Pi radians

Why does the tangent function have vertical asymptotes?

• Because the function is periodic.

• Because sine is zero.

• Because tangent is zero.

• Because cosine is zero.

What is the value of the tangent function at x = 0?

• 1

• -1

• 0

• Undefined

What are the key points to graph the tangent function over one period?

• x = 0, Pi, 2Pi

• x = -Pi/2, 0, Pi/2

• x = -Pi, 0, Pi

• x = -Pi/4, 0, Pi/4

How can the pattern of the tangent function be extended?

• By increasing the period.

• By changing the amplitude.

• By copying and pasting the graph.

• By adding more vertical asymptotes.