asked • 07/15/14

find tan theta

If cot theta = 2/3 and csc theta > 0

2 Answers By Expert Tutors


Bob A. answered • 07/15/14

4.9 (127)

20 Years Making Science and Maths Understandable and Interesting!

Katherine S.

Why the U pattern mnemonic followed by mnemonic bashing?  I tend to remember SOH-CAH-TOA and that the inverses simply flip the fractions.  Each pairing has one and only one "co," sine is standard and secant is inverse...
sine o/h --> cosecant h/o
cosine a/h --> secant h/a
tangent o/a --> cotangent a/o


Bob A.

Yea, I guess the 'U' is a mnemonic and I so I was hypocritical.
I should not have bashed mnemonics - they are great.
But here is my reasoning.
Using SOA CAH TOA   or the  Oh, Ah, Oh Ah, Ah Oh, Ha, Ho that I had to memorize in my HS trig class  you are using a mnemonic to remember all the functions.  And if learning them (visualizing them) (writing them) in a row across the page as <sin, cos, tan, cot, sec, csc> or learning/visualizing/writing them in a column down a page - then you have to remember which ones are the inverses of what.
Notice when you wrote them down to show which were reciprocals of which you wrote them down in the 'U' pattern.
If I show the student from the get-go to learn/write/visualize them always in a 'U' then the only thing that has to be memorized by blind meaningless rote is the sine and cosine.
Then everything else is put down not by blind rote; but by knowing things about the functions.
Tan = sin/cos, and the others are known as the reciprocals of the others and you don't have to memorize which are reciprocals, you can see it in the table.
Does that make since?  Your thoughts now?
And you are right I was being hypocritical.  I used a mnemonic 'U'.
What I am hoping is that the 'U' shows more meaning that trying to memorize all the other stuff and that it is easier for a beginner to get it all together.  I know you and I will say what's the difference, its all the same - because we know it.  But a beginner a bit more of a picture of what is going on - I Hope - and gets it right quicker.
BTW - I these are reciprocals not inverses.  the trig functions are one of a few places in math where the reciprocal is not the same as the inverse.  e.g. the inverse of  sin  is  sin-1  or  arcsin.
Or at least that is the way I think of it and explain it.
Happy to hear you comments now.
Wish we had a tutor to tutor PM system.
And check out "Trig without Tears" I mentioned. Good stuff to remember the trig easily.
Look at his way to remember the special angle values.
0, 30, 45, 60, 90
0, 1, 2, 3, 4
√0, √1, √2, √3, √4
then divide each by 2


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