Learn How to Graph the Cosecant Function with a Change in Period

The video tutorial covers the graphing of reciprocal functions, focusing on sine and cosecant. It explains the step-by-step process of graphing these functions without a calculator, emphasizing the importance of understanding amplitude, phase shift, and vertical translation. The tutorial also discusses the domain and range of these functions, highlighting the role of asymptotes. Additionally, it covers graph behavior, including maxima, minima, and intervals of increase and decrease.

What is the first step in graphing reciprocal functions?

• Graph the original function

• Determine the range

• Use a calculator

• Find the domain

In the formula Y = a * sin(BX - C) + D, what does 'a' represent?

• Vertical translation

• Phase shift

• Period

• Amplitude

How do you calculate the period of a sine function?

• 2π / B

• D / C

• C / D

• B / 2π

What is the phase shift if BX - C = 0 results in X = 0?

• No phase shift

• Vertical shift

• Shift to the right

• Shift to the left

When graphing sine, what is the new scale used instead of 1/2 and 3?

• 3π

• 4π

• 2π

• π

What is the relationship between sine and cosecant?

• Cosecant is the reciprocal of sine

• Cosecant is the derivative of sine

• Cosecant is the integral of sine

• Cosecant is the inverse of sine

What happens at the points where the sine graph crosses the x-axis?

• They become asymptotes for cosecant

• They become maximum points

• They become minimum points

• They become inflection points

What is the domain of the cosecant function?

• All real numbers

• Only negative numbers

• Only positive numbers

• All real numbers except where sine is zero

How is the range of the cosecant function expressed?

• (-∞, 0) ∪ (0, ∞)

• [-1, 1]

• [0, 1]

• (-∞, -1] ∪ [1, ∞)

What variable is used to represent the repetition of asymptotes in the domain?

• Z

• Y

• X

• N