Trigonometric Functions and Their Properties

The video tutorial explores how to identify and analyze trigonometric graphs, focusing on sine and cosine functions. It explains how to determine the amplitude and period of these graphs and how to derive their equations. The tutorial emphasizes understanding the number of cycles within 2π radians and encourages viewers to practice these concepts on the Khan Academy website.

What is the key difference between a sine curve and a cosine curve at x = 0?

• Sine of 0 is 1, Cosine of 0 is 0

• Both Sine and Cosine of 0 are 1

• Both Sine and Cosine of 0 are 0

• Sine of 0 is 0, Cosine of 0 is 1

What does the coefficient 'A' in a trigonometric function represent?

• The amplitude

• The phase shift

• The period

• The frequency

How do you determine the period of a trigonometric function from its graph?

• By finding the x-value where the function first reaches its minimum

• By counting the number of cycles in 1 radian

• By measuring the distance between two consecutive peaks

• By finding the x-value where the function first reaches its maximum

If a function completes four cycles in 2π radians, what is the coefficient of x in the function?

• 4

• 1

• 3

• 2

What is the amplitude of a sine function if it moves 1 unit above and below the x-axis?

• 0.5

• 2

• 1

• 1.5

How many cycles does a sine function complete in 2π radians if it completes two cycles in π radians?

• 2

• 4

• 1

• 3

What is the period of a function that completes half a cycle in 2π radians?

• 4π

• π

• 2π

• 8π

If f(0) = 0 for a trigonometric function, what type of function is it likely to be?

• Shifted sine function

• Non-shifted cosine function

• Non-shifted sine function

• Shifted cosine function

What is the formula to find the coefficient of x in a trigonometric function using the period?

• 2π divided by the period

• Period divided by 2π

• Amplitude divided by the period

• Period divided by amplitude

Why is it beneficial to understand the reasoning behind the formula for the coefficient of x?

• It is not beneficial

• It helps in memorizing the formula

• It allows re-deriving the formula without memorization

• It makes calculations faster