Cosecant Function Properties and Behavior

The video tutorial explains the cosecant function as the reciprocal of sine, highlighting key points where sine equals one and identifying asymptotes where the denominator is zero. It discusses the behavior of the cosecant function between these key points, emphasizing symmetry and periodicity over 360 degrees.

What is the reciprocal of the sine function called?

• Cotangent

• Tangent

• Cosecant

• Secant

Where do asymptotes occur in the cosecant function?

• Where sine is negative one

• Where sine is two

• Where sine is one

• Where sine is zero

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

• Infinity

• One

• Zero

• Negative one

How does the cosecant function behave at points where sine equals negative one?

• It equals zero

• It equals one

• It equals negative one

• It equals infinity

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

• It approaches zero

• It becomes undefined

• It increases significantly

• It decreases significantly

What is the behavior of the cosecant function between 0 and 180 degrees?

• It remains constant

• It decreases

• It increases

• It oscillates

What is the period of the cosecant function?

• 360 degrees

• 270 degrees

• 90 degrees

• 180 degrees

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

• Sine is more periodic

• Cosecant is more periodic

• Both have the same periodicity

• Neither is periodic

What is the effect of symmetry on the cosecant function graph?

• It causes the graph to repeat

• It creates a linear graph

• It makes the graph non-periodic

• It has no effect

What happens to the cosecant function as it approaches the asymptotes?

• It approaches infinity

• It approaches zero

• It remains constant

• It becomes undefined