Understanding Periods in Trigonometric Functions

The video tutorial explains how to find the amplitude and period of sine and cosine functions. The amplitude is the absolute value of the coefficient 'a', while the period is calculated using 2π divided by the coefficient 'B' of the input value. The tutorial emphasizes understanding fractions and simplifying them by multiplying by the reciprocal. It concludes with a discussion on input values and their coefficients.

What is the amplitude of a sine or cosine function?

• The absolute value of the coefficient 'a'

• The coefficient of the input value

• The period of the function

• The reciprocal of the coefficient 'B'

What happens to the amplitude if 'a' is negative?

• It becomes positive

• It remains negative

• It doubles

• It becomes negative

What is the effect of a negative 'a' on the graph of the function?

• It flips the graph

• It stretches the graph

• It compresses the graph

• It shifts the graph

How is the period of a trigonometric function calculated?

• 2π times the coefficient 'a'

• 2π divided by the coefficient 'B'

• The absolute value of 'a'

• The reciprocal of 'B'

What is the relationship between 'B' and the period?

• Unrelated

• Inversely proportional

• Equal

• Directly proportional

In the function y = a sin(bx), what does 'b' represent?

• The period

• The coefficient of the input value

• The phase shift

• The amplitude

What is the coefficient of the input value in y = a sin(bx)?

• a

• b

• y

• x

How can you express 2x/3 in terms of a coefficient and input value?

• x/2 * 3

• 2/3 * x

• 3/2 * x

• 2x * 3

What is the first step in simplifying a fraction division?

• Divide by the reciprocal

• Add the fractions

• Multiply by the reciprocal

• Subtract the fractions

What is the period of a function if B is 2/3?

• 4π

• π

• 2π

• 3π