Graphs of Secant and CosecantObjectives:

I can describe the relationship between the equation of a sec or csc function and its vertical stretch, period, midline, and horizontal shift. I can find the equation of a sec or csc function when given its graph.

Key Terms and Formulas: General sec or csc equation: or .Midline or Vertical Shift: c The horizontal line in between peaks and valleys.Vertical Stretch: The distance from the midline to a peak or valley. (-a flips graph vertically)Period: and The period is the length of 1 cycle, from a point to the next similar point (such as a peak to the next peak).Horizontal Shift: b The amount a graph has been shifted horizontally.

Note how the csc and sec curves are related to sin and cos curves:

ab (using sec)

cPer.

Original by Dr. Lee SingletonNSF: DRL #1623405

1. Find the period and amplitude of the following functions, then sketch the graph.Draw the appropriate sin or cos curve as a guide, then the asymptotes, then actual curve.a)

b)

c)

d)

2. Write the equation of the following graphs:a) b)

c) d)

3. Draw a secant curve centered at the midline shown below.

Equation:______________________________ Equation:______________________________

Equation:______________________________ Equation:______________________________

Draw in the x-axis and appropriate scaling on the x-axis and y-axis so your curve represents the following equation:

4. Find the period and vertical stretch, vertical shift, and horizontal shift of the following function, then sketch the graph. (Hint: Draw a midline, then draw the sin or cos guideline curve. Put in the asymptotes and sketch the graph. Find where the x-axis is and draw it in. Put labels on the x-axis, then draw in the y-axis with labels.) V.Stretch =

Per = H.S. = V.Shift. =

5. Find the period and vertical stretch, vertical shift, and horizontal shift of the following function, then sketch the graph. (Hint: Draw a midline, then draw the sin or cos guideline curve. Put in the asymptotes and sketch the graph. Find where the x-axis is and draw it in. Put labels on the x-axis, then draw in the y-axis with labels.)

V.Stretch. =Per = H.S. = V.Shift =