Study with the several resources on Docsity
Earn points by helping other students or get them with a premium plan
Prepare for your exams
Study with the several resources on Docsity
Earn points to download
Earn points by helping other students or get them with a premium plan
Solutions to problems related to finding the area of triangles and converting polar coordinates to rectangular coordinates. It also includes an application of finding the area of the Bermuda Triangle using the formula for the area of a triangle. from the Department of Mathematics at the University of Wisconsin-Madison and is for Math 114 course.
Typology: Study notes
1 / 5
This page cannot be seen from the preview
Don't miss anything!
b a
c
(a) a = 6, b = 4, C = 40◦.
Solution:
ab sin 60◦
(b) a = 4, b = 5, c = 3.
Solution:
s(s − a)(s − b)(s − c)
s =
(a + b + c)
s =
s = 6
K =
Lauderdale, Florida. The distance from Hamilton to Fort Lauderdale, Fort Lauderdale to San Juan, and San Juan to Hamilton are approximately 1028, 1046, and 965 miles, respectively. Ignoring the curvature of Earth, approximate the area of the Bermuda Triangle.
Solution:
s(s − a)(s − b)(s − c)
s =
(a + b + c)
s =
s = 1519. 5
K =
K ' 442 , 816 square miles
(a)
3 π 2
Solution:
x = r cos θ
x = 4 cos
3 π 2
x = 0
y = r sin θ
y = 4 sin
3 π 2
y = − 4
Answer: (x, y) = (0, −4)
(b) (− 3 , 3)
Solution: The point is in the second quadrant so θ will be in the second quadrant.
r =
x^2 + y^2
r =
r = 3
tan θ =
y
x
tan θ =
tan θ = − 1
θ =
3 π
4
Answer: (r, θ) =
3 π
4
(c) (
Solution: The point is in the first quadrant so θ will be in the first quadrant.
r =
x^2 + y^2
r =
r = 2
tan θ =
y
x
tan θ =
θ =
π 6
Answer: (r, θ) =
π
6
Solution: x^2 + y^2 = r^2 and x = r cos θ So r^2 = r cos θ or r = cos θ
Solution:
r = sin θ − cos θ
r^2 = r sin θ − r cos θ
x^2 + y^2 = y − x
