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Today in Pre-Calculus

This lesson covers topics such as simulating projectile motion and solving problems using polar coordinates. Topics include parametric equations, graphing parametric equations, converting between rectangular and polar coordinates, and converting equations in different coordinate systems.

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Today in Pre-Calculus

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Presentation Transcript

  1. Today in Pre-Calculus • Finish Chapter 6 review – need a calculator • Go over Chapter 9 homework • I will take your textbook any time between now and your final exam. Make sure they are cleaned out and your name is on the inside cover.

  2. Simulating Projectile Motion The path of the object is modeled by the parametric equations: x=(v0cosθ)t y= -16t2 + (v0sinθ)t +y0 Note: The x-component is simply d=rt where r is the horizontal component of v0. The y-component is the velocity equation using the y-component of v0.

  3. Example Clark hits a baseball at 3ft above the ground with an initial speed of 150ft/sec at an angle of 18° with the horizontal. Will the ball clear a 20ft fence that is 400ft away? The path of the ball is modeled by the parametric equations: The fence can be graphed using the parametric equations:

  4. Example Approximately how many seconds after the ball is hit does it hit the wall? How high up the wall does the ball hit?

  5. Ferris Wheels Nikko is riding on a Ferris wheel that has a diameter of 122ft and is suspended so the bottom of the wheel is 12ft above the ground. The wheel makes one complete revolution every 20 seconds. Where is Nikko after 15 seconds?

  6. Polar Coordinates Convert the following to rectangular coordinates 1. 2. (-1, 330°)

  7. Polar coordinates Convert the following to polar coordinates (find all in the given interval) 1. (1, 1) ( 0≤ θ≤ 2π) 2. (-2, 5) (-π≤θ≤π)

  8. Polar graphs

  9. Converting Equations Convert to rectangular, and identify the equation r = 2cosθ + 2sinθ

  10. Converting Equations Convert to polar and identify the equation. (x – 2)2 + y2 = 4

  11. Homework • Pg 562: 17,18, 21, 53-60, 61-67odd, 80,81,82 assume they start at the bottom 84,85

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