Please offer your submissions for any of the sections below – comments, questions, inspirational story, joke, puzzle, math news, or specific job information. It really may be of value to someone.

Send to: submissions@trickytrig.com

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QUARTERLY SAMPLE:

**QUARTERLY COMMENTS **

I have liked everything about this course. Going at my own pace, looking back at your examples as I needed when working the exercises and having plenty of practice problems really helped me learn Trig thoroughly, I feel. Thank you.

-Tom M., CO

This e-course was obviously home-spun, without bells and whistles. That bothered me at first, but your straight-forward, simple explanations with an emphasis on 'thinking about it' instead of drawing perfect figures soon won me over. Your knowledge is what counted; I learned a lot.

-Joe T., AZ

**QUARTERLY QUESTIONS**

The idea of the Principal functions and Inverses in composite functions confused me most. What can I do?

-Mike C., MD

ANSWER: Realize it’s just the 2 basic problems (Sin A = __, Sin^{-1}x = ___, for example) back and forth many times. Make a right triangle (or use a calculator) to answer each step, work from right to left – but be sure you always think “Is it defined?” first. (That’s usually the problem – not knowing the angle and value restrictions.) If it’s “out of bounds” at any step, then your answer is “undefined” and you can stop there!

**QUARTERLY PROBLEM**

I will give you a simple composite function problem (no calculator or triangles needed, unless you want to) – just write down what you know and are trying to find for each step):
Sin(Csc^{-1}(Tan(Cot^{-1}(Sin(Sin^{-1}(Cos(Sec^{-1}(5/4)))))))) = ________?
(Answer at the end.)

**QUARTERLY TOPIC**

I would like to present you with another “special” Polar Graph (to again emphasize radian measurement, even though most of the time we may think degrees as we graph around the circle.)
To graph r = theta , it’s impossible to think of the radius of a circle being 30°, say. But if we think of theta in radians – a number like π
/4 is easily thought of both as a value for “r” (3.14/4 = .785) and as an angle (45°), the point
(r, theta) being what we plot on our polar coordinate system. Notice that we are NOT taking the sine or cosine of the angle here.

Problem: Make a table for “r” and “theta”, beginning at 0, going by π
/2s and continuing to 4π
. (We normally need only to go to 2π, or less if we see the pattern, so this is also different.) Graph r = theta (curving counterclockwise from point to point, remember). (Answer at the end.)

**QUARTERLY QUOTE**

“Genius is 10% inspiration and 90% perspiration”. Albert Einstein

**QUARTERLY THOUGHT**

Many times people think others can do things a lot easier than they can. And perhaps that’s true. But to really accomplish whatever your goal is, I’ve found that just plain old hard work, determination, and perseverance will get the job done – whether it’s digging a ditch, doing a huge pile of dishes, or working a math problem. In the process of inventing the light bulb, Thomas Edison is said to have replied to someone asking how he kept on working without becoming discouraged, “I’ve found 1000 things that don’t work”. Keeping at it one step at a time, putting one foot in front of the other, continuing to work on it – these are the steps that will finally produce the result: “Hey, it’s finished, and I’ve done it!”

**QUARTERLY INSPIRATION**

While watching my son, Martin, run a race at a track meet, and knowing how badly he wanted to win to advance to higher competition, I was shocked when Martin, in the lead, stopped when his chief rival fell, helped him up, and literally pushed him across the finish line first. He grinned and cheered when Tom was given the gold.
Later, I asked Martin why he had come in second on purpose. “One time, I fell in a race and wouldn’t get back up. Tom had the courage to get up and go on. He deserved to win!” Martin was right. Winners were people who got up and went on after a fall. And he had done it at the Special Olympics. You see, wise, loving Martin is “mentally challenged”.
-Condensed, from Nancy Tiemann, IL

**QUARTERLY POEM**

STRENGTH

YOU ARE OUR HELP IN ALL WE DO,

GIVING US STRENGTH TO SEE US THROUGH;

YOU NEVER FAIL; YOU’RE ALWAYS THERE.

HELP US KNOW IT, O GOD – OUR PRAYER!

JFD, from “WORDS FROM WITHIN”

**QUARTERLY MATHEMATICIAN**

The first significant contributions to the subject of trigonometry were made by the Greeks. Hipparchus of Nicaea (c. 190 B.C.), a mathematician and astronomer, did most of his work on the island of Rhodes and was the first to make systematic use of trig, making tables of chord lengths of angles, and there is evidence that he made use of relationships similar to some of those in modern trigonometry, as well as spherical trigonometry. He computed the distance to the moon as being 59 earth radii – very close (the true mean distance actually being about 60.3). Hipparchus is generally considered as the actual founder of trigonometry.

**QUARTERLY JOKE**

Baby-sitting our 3-year-old granddaughter one day, I asked her mother if she could have some ice cream later. “A little bit,” she replied.
Several hours later, when I served Ridley a generous portion of ice cream, she observed, “That’s too much, Granddaddy”. “Just eat what you can,” I absent-mindedly replied, busy with something else.
A few minutes later, Ridley announced, “I’ve eaten the ‘too much’ part; now I’ll eat the ‘little bit’.” And she did.

**QUARTERLY BRAIN-TEASER**

This section will consist of different kinds of puzzles – not too difficult or time-consuming, but hopefully fun. I’ll begin with a simple one: Unscramble the letters to spell words used in this Trigonometry course. (Answers at the end)

ORPAL ________________________

TCCNEOA ________________________

RESNEIV ________________________

TCCOONNUIF ________________________

PSTAEMTYO ________________________

AHOTGYANEPR ________________________

MELICTARNO ________________________

**QUARTERLY “MATH IN THE MEDIA” **

The Hubble telescope, launched in 1990 and just recently finished being repaired with Service Mission 4, has given us, with its remarkable pictures, a new view of the universe (and “dark energy”). The size of a large school bus (43.5 ft (13.2 m) long and 14 ft (4.2 m) in diameter), it travels at 5 miles/sec (from LA to NYC by car in 10 minutes), sweeps the Earth every 97 minutes from an altitude of 374 miles (561km) – using the energy of 28 100W light bulbs per orbit -- and travels 150 million miles (241 million km) each year.

**QUARTERLY MATHEMATICAL JOBS **

The basic question of all math students is “How am I ever going to use this?” Here are some answers – with sites for information listed:

Online Teaching jobs (& tutor) -- GetEducated.com

Math coordinator: Ravenswood City Elementary, CA, $69202 -- edjoin.org

Occupational outlook -- bls.gov/oco/ocos043.html

Careers in math (links) -- cln.org/themes/careers_math.html

Full and Part-time faculty positions at colleges across the U.S. -- higheredjobs.com

Articles on choosing a career -- associatedcontent.com

Volunteer and/or Tutor ($50/hr?) at your local high school or college to get wonderful experience and really learn your subject.

**ANSWERS: 4/5; a spiral; polar, cosecant, inverse, cofunction,
asymptote, Pythagorean, coterminal **