Original by Dr. Lee Singleton NSF: DRL #1623405 Graphs of Secant and Cosecant Objectives: 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. a b (using c Per.
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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.
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.)