GBK Precalculus Jordan Johnson

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GBK Precalculus Jordan Johnson. Today’s agenda. Greetings Review / Submit HW: Section 4-5 (pp. 180-182): Reading Analysis questions. Exercises Q1-Q10. Exercises 1-9 odd, 15-19 odd. Lesson: More Parametric Functions Homework Clean-up. Two related functions. x = sec t , y = tan t

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GBK PrecalculusJordan Johnson

Today’s agenda
• Greetings
• Review / Submit HW: Section 4-5 (pp. 180-182):
• Exercises Q1-Q10.
• Exercises 1-9 odd, 15-19 odd.
• Lesson: More Parametric Functions
• Homework
• Clean-up
Two related functions
• x = sec t, y = tan t
• Degree mode
• t [0°, 360°]
• t-step = 1
• Eliminate the parameter (using a trig identity).
• Modify the parametric equations to dilate it vertically & horizontally by 5 and 3 (resp.) and center it at (-2, 1).
• x = tan t, y = sec t
• What do you predict this will look like?
• Graph it.
A small menagerie of functions
• A cycloid:
• x = t – sin t
• y = 1 – cos t
• An epicycloid:
• x = 5 cos t – cos 5t
• y = 5 sin t – sin 5t
• A witch of Agnesi:
• x = 2 cot t
• y = 2 sin2t

Maria Agnesi 1718-1799

Homework
• From Section 4-5: Exercises 11, 13, 16, 22.
• Due tomorrow, 1/11/11.
Clean-up / Reminders
• Pick up all trash / items.
• Push in chairs (at front and side tables).
• See you tomorrow!