Anonymous answered • 07/15/14

Tutor

tanθ = 1 / cotanθ

If cotanθ = 2/3 ... Then tanθ = 3/2.

SHEILY A.

asked • 07/15/14If cot theta = 2/3 and csc theta > 0

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Anonymous answered • 07/15/14

Tutor

tanθ = 1 / cotanθ

If cotanθ = 2/3 ... Then tanθ = 3/2.

Bob A. answered • 07/15/14

20 Years Making Science and Maths Understandable and Interesting!

Tutor

You should remember your trig functions in this way.

In a 'U' pattern, going down SIN, COS, TAN,

then to the right going up, COT, SEC, CSC

<the order is sin, cos, tan, cot, sec, csc>

Like this:

SIN **↓ ↑** CSC

COS **↓ U ↑** SEC

TAN →→ ↑ COT

Then learn that sine = Opp/Hyp and cosine = Adj/Hyp

OR - from the mnemonic SOH and CAH

or pretend you are watching fireworks -- Oh! Ah!

you don't need the rest of the mnemonic (TOA) , it is kind of useless,

and it gets in the way and will only cause you Not To Remember the important things.

If you are trying to memorize things from a mnemonic you are learning

them with a blindfold and do not learn how to understand them.

Then learn that Tangent = Sine/Cosine

Sine over cosine is Much more useful than Opp/Adj , and

if you divide sin/cos you get Opp/Adj anyway, so you can find it easily when needed.

Now you have:

SIN = Opp/Hyp CSC

COS = Adj/Hyp SEC

TAN = sin/cos = Opp/Adj COT

COS = Adj/Hyp SEC

TAN = sin/cos = Opp/Adj COT

Now learn that the trig functions on the right are the reciprocal of those on the left

Now you have:

SIN = Opp/Hyp CSC = 1/sin = Hyp/Opp

COS = Adj/Hyp SEC = 1/cos = Hyp/Adj

TAN = sin/cos = Opp/Adj COT = 1/tan = cos/sin Adj/Opp

SIN = Opp/Hyp CSC = 1/sin = Hyp/Opp

COS = Adj/Hyp SEC = 1/cos = Hyp/Adj

TAN = sin/cos = Opp/Adj COT = 1/tan = cos/sin Adj/Opp

It is MUCH easier to remember the important things about the trig functions this way.

Now can you see that if cot θ = 2/3 that tan θ = 3/2

Remember your trig functions like that and you won't ever have to ask again.

For even more goodies and ways to easily remember trig identities and formulas

Look on the internet for "Trig Without Tears" by Stan Brown

http://oakroadsystems.com/twt/

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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07/16/14

Katherine S.

07/16/14