Trigonometric Graph Transformations

The video tutorial covers the basic trigonometric graphs: sine, cosine, and tangent. It explains their characteristics, such as intercepts and ranges, and demonstrates how to transform these graphs through scaling, shifting, and phase shifts. The tutorial provides a comprehensive understanding of how to manipulate trigonometric graphs for different mathematical applications.

What is the range of the sine function from 0 to 360 degrees?

• -1 to 1

• 0 to 2

• -2 to 2

• 0 to 1

How does the cosine graph differ from the sine graph?

• It is shifted 90 degrees to the left

• It is shifted 90 degrees to the right

• It has a different range

• It starts at the origin

What happens to the sine graph when a coefficient of 2 is placed in front?

• The range becomes -2 to 2

• The graph flips

• The period doubles

• The graph shifts up

If the coefficient in front of the sine function is 3, how many cycles will fit in the standard domain?

• 1 cycle

• 4 cycles

• 2 cycles

• 3 cycles

What is the effect of adding a constant to the sine function?

• It changes the period

• It flips the graph

• It shifts the graph vertically

• It changes the range

How does a negative sign in front of the sine function affect the graph?

• It shifts the graph up

• It shifts the graph to the right

• It changes the period

• It flips the graph over the x-axis

What is the new range of a sine graph if it is shifted up by 1 unit?

• 0 to 2

• -2 to 2

• -1 to 1

• 1 to 3

What is a phase shift in trigonometric graphs?

• A vertical stretch

• A change in range

• A horizontal shift

• A change in frequency

If a sine graph is shifted 60 degrees to the right, what is the actual shift if the function is 3x?

• 60 degrees

• 90 degrees

• 20 degrees

• 180 degrees

What is the term used for the horizontal shift in a repeating trigonometric graph?

• Frequency shift

• Vertical shift

• Phase shift

• Amplitude change