Graph Cosecant: Phase shift and reflection

The video tutorial covers transformations in trigonometric functions, focusing on reflections, phase shifts, and range. It explains how these transformations affect the graph of functions like sine and cosecant. The tutorial also delves into vertical asymptotes, discussing how they shift with transformations and how to simplify their equations. The instructor emphasizes understanding these concepts to avoid common misconceptions and prepare for more advanced topics.

What is the effect of multiplying a trigonometric function by a negative value on the outside?

• It shifts the graph to the right.

• It compresses the graph vertically.

• It reflects the graph about the X-axis.

• It stretches the graph horizontally.

What is the significance of the phase shift in the context of trigonometric transformations?

• It reflects the graph about the Y-axis.

• It alters the period of the function.

• It changes the amplitude of the function.

• It shifts the graph horizontally.

How does a reflection about the origin affect the graph of an odd function like cosecant?

• It compresses the graph horizontally.

• It has no effect on the graph.

• It shifts the graph upwards.

• It changes the graph completely.

How does the range of the sine function compare to that of the cosecant function?

• Sine has a larger range than cosecant.

• Sine's range is from negative infinity to infinity.

• They have the same range.

• Cosecant's range is from negative infinity to -1 and from 1 to infinity.

What is the relationship between the sine and cosecant functions in terms of their range?

• They have identical ranges.

• Cosecant's range is the inverse of sine's range.

• Cosecant's range is narrower than sine's.

• Sine's range is broader than cosecant's.

What happens to the vertical asymptotes of a trigonometric function when the graph is shifted?

• They move according to the shift.

• They double in number.

• They remain unchanged.

• They disappear.

Why can the negative sign in the expression for asymptotes sometimes be omitted?

• Because it simplifies the expression without changing the values.

• Because it makes the expression more complex.

• Because it changes the range of the function.

• Because it is not mathematically valid.