ACT SAT Prep How do the graphs of two trigonometric graphs compare

The video tutorial discusses how to compare the graphs of y = cosine(θ) and y = 2cosine(θ). It explains the concept of graph transformations, focusing on amplitude and period changes. The teacher uses familiar algebraic functions to illustrate these transformations, emphasizing the effects of multiplying by a constant. The tutorial concludes by highlighting that multiplying the cosine function by 2 affects the amplitude but not the period.

What is the first step in solving a problem when you have no idea what to do?

• Guess the answer

• Ask a friend

• Underline important information

• Skip the problem

How does multiplying by 2 affect the graph of y = |x|?

• It compresses the graph horizontally

• It stretches the graph vertically

• It shifts the graph right

• It shifts the graph left

What does the initial period of the cosine graph look like?

• A parabolic curve

• A straight line

• A continuous wave

• A zigzag pattern

Which option is NOT a possible comparison for the graphs y = cos(θ) and y = 2cos(θ)?

• Twice the period, same amplitude

• Half the amplitude, same period

• Half the period, same amplitude

• Twice the amplitude, same period

What is the effect of multiplying a function by 2 on its amplitude?

• It halves the amplitude

• It doubles the amplitude

• It has no effect on the amplitude

• It triples the amplitude

What does the absolute value of a represent in a trigonometric function?

• The period

• The phase shift

• The frequency

• The amplitude

What remains unchanged when a trigonometric function is multiplied by a constant?

• The frequency

• The period

• The amplitude

• The phase shift