Today in Pre-Calculus• Review Chapter 6 – need a

calculator• We’ll go over Chapter 9

homework tomorrow.• 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.

Simulating Projectile MotionThe 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.

ExampleClark 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:

ExampleApproximately how many seconds after the ball is hit does it hit the wall?

How high up the wall does the ball hit?

Ferris WheelsNikko 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?

Polar CoordinatesConvert the following to rectangular coordinates

1.

2. (-1, 330°)

54,

4

Polar coordinatesConvert the following to polar coordinates (find all in the given interval)

1. (1, 1) ( 0≤ θ ≤ 2π)

2. (-2, 5) (-π ≤ θ ≤ π)

Polar graphs

Converting EquationsConvert to rectangular, and identify the equation

r = 2cosθ + 2sinθ

Converting EquationsConvert to polar and identify the equation.

(x – 2)2 + y2 = 4

Homework• Pg 562: 17,18, 21, 53-60, 61-67odd,

80,81,82 assume they start at the bottom

84,85