Effects of Transformations on Trigonometric Functions

The video tutorial explains how to graph the cosecant and secant functions by using their reciprocal relationships with sine and cosine. It starts with basic graphing techniques for sine and cosine, identifying vertical asymptotes where the functions are undefined. The tutorial then progresses to more complex examples, including transformations such as amplitude changes, phase shifts, and vertical shifts. The video emphasizes using sine and cosine graphs as guides to accurately plot cosecant and secant graphs.

What is the reciprocal function of sine?

• Secant

• Cosecant

• Cosine

• Tangent

What is the relationship between the sine and cosecant graphs?

• Cosecant is the integral of sine

• Cosecant is the derivative of sine

• Cosecant is the reciprocal of sine

• Cosecant is the inverse of sine

What happens to the cosecant graph at points where the sine graph is zero?

• It becomes zero

• It has a vertical asymptote

• It reaches a minimum

• It reaches a maximum

How do you determine the vertical asymptotes for the cosecant graph?

• Where sine is maximum

• Where sine is minimum

• Where sine crosses the x-axis

• Where sine is undefined

What is the reciprocal function of cosine?

• Tangent

• Secant

• Sine

• Cosecant

What is the relationship between the cosine and secant graphs?

• Secant is the integral of cosine

• Secant is the derivative of cosine

• Secant is the reciprocal of cosine

• Secant is the inverse of cosine

Where do vertical asymptotes occur in the secant graph?

• Where cosine is maximum

• Where cosine is minimum

• Where cosine crosses the x-axis

• Where cosine is undefined

How do you graph the secant function using the cosine graph?

• Graph cotangent and invert it

• Graph tangent and invert it

• Graph sine and invert it

• Graph cosine and invert it

What is the period of the function y = 2 sine (1/2 X)?

• π

• 4π

• 2π

• 8π

What is the amplitude of the function y = 2 sine (1/2 X)?

• 4

• 2

• 1/2

• 1