Understanding Trigonometric Functions

The video tutorial explains how to identify a trigonometric function from its graph by determining its amplitude and period. It guides the viewer through the process of distinguishing between sine and cosine functions based on their values at specific points. The tutorial also compares sine and cosine functions, highlighting their differences and similarities. The video concludes with a brief mention of using a graphing module for further exploration.

What is the first step in identifying a trigonometric function from its graph?

• Identify the function's x-intercepts

• Determine the function's amplitude and period

• Calculate the function's derivative

• Find the function's maximum value

How is the amplitude of a trigonometric function defined?

• The total distance the graph covers

• The distance from the y-axis to the peak of the graph

• The distance from the x-axis to the peak of the graph

• The distance between two consecutive peaks

What is the period of a trigonometric function?

• The time it takes to complete one full cycle

• The distance between two consecutive peaks

• The time it takes to reach the maximum value

• The distance from the x-axis to the peak

How can you determine if a function is sine or cosine based on its value at zero?

• If the function value is 1, it is cosine

• If the function value is 0, it is sine

• If the function value is 0, it is cosine

• If the function value is 1, it is sine

What is the formula for the sine function derived in the video?

• f(x) = cos(x)

• f(x) = sin(x)

• f(x) = 1/2 sin(2x)

• f(x) = 1/2 cos(2x)

What is the value of g(0) for the function g(x) = 1/2 cos(2x)?

• 0

• 1

• 1/2

• 2

How does the graph of g(x) = 1/2 cos(2x) differ from f(x) = 1/2 sin(2x)?

• It has a different amplitude

• It has a different period

• It is shifted horizontally

• It is shifted vertically

Why does the graph of g(x) = 1/2 cos(2x) intersect the y-axis at 1/2?

• Because cosine of 0 is 1

• Because sine of 0 is 0

• Because of the 1/2 coefficient

• Because of the period of pi

What is the significance of the coefficient in front of the cosine function?

• It determines the period

• It determines the amplitude

• It determines the phase shift

• It determines the frequency

What tool is mentioned for further exploration of trigonometric graphs?

• Online graphing tool

• Mathematical software

• Khan Academy trig graphing module

• Graphing calculator