Cosecant Function and Its Properties

The video tutorial explains the concept of the cosecant function as the reciprocal of sine. It highlights the presence of asymptotes where the sine function is zero and discusses the behavior of the cosecant graph, including its symmetry and periodicity. Key points where sine equals one or negative one are identified, and the graph's behavior is analyzed as it approaches these points. The tutorial concludes with an understanding of the periodic nature of the cosecant function over 360 degrees.

What is the reciprocal of the sine function known as?

• Cosecant

• Cotangent

• Secant

• Tangent

What happens to the graph of a function at an asymptote?

• It approaches infinity

• It crosses the axis

• It becomes zero

• It remains constant

At which angles does the sine function have asymptotes in the cosecant graph?

• 0, 90, 180

• 90, 270

• 0, 180, 360

• 45, 135, 225

What is the reciprocal of 1 in the context of the sine function?

• Infinity

• -1

• 1

• 0

What is the reciprocal of -1 in the context of the sine function?

• Infinity

• -1

• 1

• 0

What happens to the cosecant function as the sine value approaches zero?

• It becomes undefined

• It approaches infinity

• It approaches zero

• It remains constant

How does the cosecant function behave between 0 and 180 degrees?

• It oscillates

• It increases

• It remains constant

• It decreases

What is the behavior of the cosecant function as it approaches 90 degrees from the left?

• It remains constant

• It decreases

• It oscillates

• It increases

What is the effect of a small denominator on the value of a fraction?

• It has no effect

• It increases the value

• It makes it zero

• It decreases the value

What is the reciprocal of the sine function at 90 degrees?

• -1

• Infinity

• 1

• 0