Assignment 86

"An approximate answer to the right question is worth a good deal more than the exact answer to an approximate question." - (John Tukey)

Math History Tidbit:

Charles Lutwidge Dodgson (1832-1898) wrote under the pseudonym Lewis Carroll. As most folks know, he authored the famous children's classics Alice's Adventures in Wonderland and Through the Looking-Glass. Less well know is the fact that he was an outstanding mathematician. He authored books and pamphlets on mathematical subjects, including Enunciations of Euclid (1863), Guide to the Mathematical Student (1864), Euclid and His Modern Rivals (1879), and Euclid I and II (1882). His publication Pillow Problems is a collection of 72 mathematical problems involving arithmetic, algebra, geometry, trigonometry, calculus, and probability.

Herkimer's Corner

When Herkimer was the leader of a blood drive, why did he wear suspenders?

Answer: He didn't want to get caught with his pints down.

Herky's friends:

MRS. SIPPI: A lady who preferred to live in the southeastern part of the U.S.

AL ABAMA: A neighbor of Mrs. Sippi.

IDA HOE: A farm girl who preferred to live in the Pacific Northwest.

ASSIGNMENT #86

Reading: Section 13.3, pages 784-786.

Written: Page 788/5-21.

Items for reflection:

Mathematical fact:
A piece of newspaper is approximately 0.008 inches. If you had a pile of 250 sheets of newspaper, how high would the pile be?

Answer: It would be approximately 142,000,000 miles high. Note: The Sun is approximately
93,000,000 miles from earth.

An angle q is in standard position if

(a) its vertex is at the origin, and
(b) one side (the initial side) coincides with the positive x-axis.
(c) the other side (the terminal side) simply needs to be a ray with (0,0) as its starting point.

If an angle q is in standard position, and if (x,y) is a point on the terminal side, then the trig functions of the angle are defined as indicated in the table:

Situation: (x,y) is on terminal side of q and r = (x2 + y2).

Example: (-3,4) is on the terminal side of q and r = [(-3)2 + 42] = 5.

sinq = y/r

sinq = 4/5

cosq = x/r

cosq = -3/5

tanq = y/x if x is not zero

tanq = -4/3

cscq = r/y if y is not zero

cscq = 5/4

secq = r/x if x is not zero

secq = -5/3

cotq = x/y if y is not zero

cotq = -3/4

Problem: How many of the six trig functions have the set of real numbers as their domain?

Solution (with communication): Only two. If x is the measure of an angle, then only sin(x) and cos(x) are defined for all real values of x. The functions csc(x) and cot(x) are undefined whenever sin(x) = 0. The functions sec(x) and tan(x) are undefined whenever cos(x) = 0.

Problem: (a) Convert 70o to radians; (b) convert 13 radians to degrees.

Solution (with communication):

(a) 70o = 70( p/180) radians, or about 1.22 radians.

(b) 13 radian = 13(180/ p )o, or about 744.85o.