find tan theta

Question

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

 

Answer 1

tanθ = 1 / cotanθ

If cotanθ = 2/3 ... Then tanθ = 3/2.

Answer 2

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

 

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

 

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/