trig_m12_handouts

# trig_m12_handouts - MAC 1114 Module 12 Polar and Parametric...

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1 Rev.S08 MAC 1114 Module 12 Polar and Parametric Equations 2 Rev.S08 Learning Objectives Upon completing this module, you should be able to: 1. Use the polar coordinate system. 2. Graph polar equations. 3. Solve polar equations. 4. Convert between a polar equation and a rectangular equation. 5. Graph a plane curve defined parametrically. 6. Find an equivalent rectangular equation for the plane curve. 7. Use parametric equations to solve applications. ht p:/ faculty.valenciacc.edu/ashaw/ Click link to download other modules. 3 Rev.S08 Polar and Parametric Equations ht p:/ faculty.valenciacc.edu/ashaw/ Click link to download other modules. - Polar Equations and Graphs - Polar Equations and Graphs - Parametric Equations, Graphs, and - Parametric Equations, Graphs, and Applications Applications There are two major topics in this module:

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2 4 Rev.S08 Polar Coordinate System ht p:/ faculty.valenciacc.edu/ashaw/ Click link to download other modules. The polar coordinate system is based on a point, called the pole , and a ray, called the polar axis . 5 Rev.S08 Rectangular and Polar Coordinates ht p:/ faculty.valenciacc.edu/ashaw/ Click link to download other modules. If a point has rectangular coordinates ( x , y ) and polar coordinates ( r , θ ) , then these coordinates are related as follows. 6 Rev.S08 Example ht p:/ faculty.valenciacc.edu/ashaw/ Click link to download other modules. Plot the point on a polar coordinate system . Then determine the rectangular coordinates of the point. P (2, 30 ° ) r = 2 and θ = 30 ° , so point P is located 2 units from the origin in the positive direction making a 30 ° angle with the polar axis.
3 7 Rev.S08 Example (Cont.) ht p:/ faculty.valenciacc.edu/ashaw/ Click link to download other modules. Using the conversion formulas: The rectangular coordinates are 8 Rev.S08 Another Example ht p:/ faculty.valenciacc.edu/ashaw/ Click link to download other modules.

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trig_m12_handouts - MAC 1114 Module 12 Polar and Parametric...

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