MATH 1151 --- 11.1.12 Discussion
1.) On a map, Orlando is 178 mm due south of Niagara Falls, Denver is 273 mm from Orlando, and Denver is 235 mm from
Niagara Falls. Find the bearing of Denver from Orlando. Find the bearing of Denver from Niagara Falls.
2.) On a baseball diamond with 90-foot sides, the pitcher’s mound is 60.5 feet from home plate. How far is the pitcher’s mound
from third base?
C
Challenge:
Compute the lengths CD and CE. (2 decimal places)
43
E
D
34
A
52
75
27
B
3.) a. What is the formula for area of a SAS triangle?
b. What is the formula for area of a SSS triangle?
4.) Find the area of the segment of a circle whose radius is 5 inches, formed by a central angle of 40°.
5.) The dimensions of a triangular lot are 100 feet by 50 feet by 75 feet. If the price of such land is $3 per square foot, how
much does the lot cost?
1.) If P is a point with polar coordinates (r,θ), the rectangular coordinates (x,y) of P given by
x=
and y =
Steps for Converting from Rectangular to Polar Coordinates
1. Always plot the point (x,y) first.
2. If x = 0 or y=0, use your illustration to find (r,θ).
3.
4.
If x≠0 and y≠0, then
√
.
To find θ, first determine the quadrant in which the point lies.
Quadrant I or IV:
Quadrant II or III:
Two Common Techniques for Transforming Equations from Polar to Rectangular Form
1. Multiplying both sides of the equation by r
2. Squaring both sides of the equation
2.) Plot each point given in polar coordinates.
a.
(4, 270°)
b. (5,
3.) Find the rectangular coordinates of (-2,
)
).
4.) Find the polar coordinates for (1.3, -2.1).
5.) Write
6.) Write
using polar coordinates (r, θ).
using rectangular coordinates (x, y).
c. (-3,