## Mathochism: Piecewise frustrations

**One woman’s attempt to revisit the math that plagued her in school. But can determination make up for 25 years of math neglect?
**

We had our first quiz today. It was a precalculus review. We were supposed to have it last Thursday, but the professor was behind on the material, so we got a reprieve and a chance to really study over the long weekend.

I used that time to bone up on my inequalities, my trig identities and root functions. I spent a total of 12 hours or so, fueled by a pan of brownies, madeleines and tea, poring over various books, including the excellently comprehensive summer pre-calc book.

I didn’t get a great night’s sleep last night, though, partly because I sleep poorly when I’m nervous, partly because there was a problem in the professor’s trig review I just couldn’t solve, and partly because my spouse is sick, or allergic, or something, and snored and wheezed all night. Normally, I deal with his snoring by shoving him somewhat gently, but he had been so miserable all yesterday that I didn’t have the heart. Also, payback is a bitch.

Still, I did get some sleep, and spent the morning just going over stuff I just needed to memorize. And I got a bottle of Peach Snapple Ice Tea, because that has become a ritual on test days.

So, the quiz. Here are the positives:

1) It was completely fair in testing material we had actually gone over, but not ridiculously simple.

2) I aced the trig part, which I had been agonizing over (see problem I couldn’t solve, above).

3) I was able to apply math test anxiety techniques I learned earlier this year, including the brain dump and staying away from nervous classmates (though I was tempted to smack one loud fretter in the hall).

4) It is a quiz, not a test, so tanking this is not a tragedy.

The negatives:

1) I have some sort of block about piecewise equations, which makes me forget simple concepts like y = 4 is a horizontal line.

2) I over-thought the f of g problem. I set it up right, but simplified it too much, multiplying things out that were best left alone, and in the process, forgot to identify zeroes in the domain. Urrgh.

3) I got the transformation on a root function graph right, but skipped a step. My answer is correct, but the professor will likely take off points.

4) I misplaced a negative sign in a slope equation, which is infuriating.

Since we went over the quiz after we took it, I know what mistakes I made. Most can be attributed to nervousness, not to a lack of understanding of the subject. This is a good thing. Last weekend, when I was testing myself on all the concepts, I was gratified to see I scored solidly in the 90th percentile. I just need to plug on.

So far, this professor is giving me a much better vibe. I hope it lasts!

PS: Can any kind mathematician out there help with this problem? I actually went to a tutor before the test, but a lot of students were in line before me, and he didn’t have time to help me before class. Fortunately, that example was not on the quiz!

Verify 2 sin x²(π/4 – x/2) = 1 – sin x

2(sin π/4 – sin x/2)² = 1 – sin x ( Working just with the left side, I rearranged it, recognizing it as an addition identity)

2(√2/2 cos x/2 – √2/2 sin x/2)² = 1 – sinx (I applied the addition identity, and turned sin π/4 and cos π/4 into √2/2.)

(√2 cos x – √2 sin x) (√2cos x – √2 sin x) = 1 – sin x (I got rid of the 2 at the front.)

2 cos² x – 4 cos x sin x + 2 sin² x = 1 – sin x (I multiplied out the expression.)

cos² x – 2 cos x sin x + sin² x = 1 – sin x (I divided by two.)

1 – 2 cos x sin x = 1 – sin x (I recognized the Pythagorean identity, and simplified.)

1 – sin 2x = 1 – sin x (I recognized the double angle sine identity, and simplified.)

1 – sin 2x does not equal 1 – sin x!!!

Help, kind mathematicians! What did I miss?

*All text copyrighted by A.K. Whitney, and cannot be used without permission.
*

In going from

“2(sqrt2/2cosx/2 -sqrt2/2sinx/2)^2 = 1 – sinx (I applied the addition identity, and turned sin p1/4 and cos pi/4 into sqrt2/2.)”

to

“(sqrt2cosx – sqrt2sinx) (sqrt2cosx – sqrt2sinx) = 1 – sinx (I got rid of the 2 at the front.)”

you got rid of too many twos.

The second line here should be

(sqrt(2) cos(x/2) – sqrt(2) sin(x/2)) *(sqrt(2)cos(x/2) – sqrt(2)sin(x/2) = 1 – sin(x).

Otherwise, it looks fine.

Thank you! I’ll try again.