Calculating Periods of Trigonometric Functions

Dan the tutor explains how to determine the period of sine and cosine functions. He describes the period as the time it takes for a graph to return to the same point. Using examples, he shows how to find periods on graphs and calculate them from equations. He also discusses scenarios with half and quarter periods, emphasizing the formula 2π/B for equations.

What is the period of a sine graph if the distance between two repeating points is 4 units?

• 4 units

• 2 units

• 6 units

• 8 units

If a sine graph shows a half period of 2π, what is the full period?

• π

• 4π

• 2π

• 3π

If a graph shows a quarter period of 6 units, what is the full period?

• 12 units

• 18 units

• 24 units

• 30 units

How do you calculate the period of a function y = cos(3x)?

• 2π/3

• π/3

• 3π

• 2π

What is the formula to find the period of a sine or cosine function given by y = cos(Bx)?

• B/π

• 2π/B

• π/B

• B/2π

What is the period of the function y = sin(x/2)?

• 2π

• 4π

• 8π

• π

In the function f(x) = 2sin(πx) + 3, what is the period?

• 2

• 1

• 2π

• π

What happens to the period of a sine function if the coefficient of x is halved?

• The period is tripled

• The period remains the same

• The period is doubled

• The period is halved

In the equation y = 2sin(πx) + 3, which part affects the period?

• 3

• None of these

• π

• 2

What is the period of y = cos(x/3)?

• 3π

• 6π

• π

• 2π