# Help How can I find acute Angle theta?

1. Aug 12, 2011

### krautkramer

Help !! How can I find acute Angle theta??

How to find acute angle theta ,when tan 63 Degree = cot theta??Could anyone help me to find answer of this query.I need steps too as I am sooooo poor in mactematicuos .Final Answer of theta should be in degrees

Last edited: Aug 12, 2011
2. Aug 12, 2011

### krautkramer

Help !! How can I find acute Angle theta??

1. The problem statement, all variables and given/known data

Help !! How can I find acute Angle theta??
How to find acute angle theta ,when tan 63 Degree = cot theta??Could anyone help me to find answer of this query.I need steps too as I am sooooo poor in mactematicuos .Final Answer of theta should be in degrees

2. Relevant equations

I don't know,If I know these things,then I would have been the head of 'NASA' :)

3. The attempt at a solution

3. Aug 12, 2011

### Staff: Mentor

Re: Help !! How can I find acute Angle theta??

First step, instead of cot write it as tan, you are probably more comfortable with tan.

Last edited: Aug 12, 2011
4. Aug 12, 2011

### PeterO

Re: Help !! How can I find acute Angle theta??

tan, is short for tangent
cot is short for co-tangent - which is short for complementary-tangent.

In the same way sin and cos are short for sine and complementary-sine

In the case of sine and cosine, the sine of an angle, and the complementary-sine of the complementary angle are equal in value.

eg, 41 degrees and 49 degrees are complementary [they add up to 90]

compare sin 41 to cos 49 - or if you prefer sin 49 to cos 41.

The relationship between tan and cot is the same.

Last edited: Aug 12, 2011
5. Aug 12, 2011

### krautkramer

Re: Help !! How can I find acute Angle theta??

Hi,thank you friends for the help,but it is not adequate to solve my problem.

I know simple mathematics like sin/cos=tan and cos/sin=cot, but not able to find a solution for my critical problem.

I will repeat the query once again...Hope you can help me....

Determine the acute angle θ when tan 63° = cot θ.

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6. Aug 12, 2011

### krautkramer

Re: Help !! How can I find acute Angle theta??

Nobody here to help me out...

7. Aug 12, 2011

### thebiggerbang

Re: Help !! How can I find acute Angle theta??

It's simple.

Use the given equation to obtain
tan(63)=cot$\theta$
arccot(tan(63))=$\theta$

Solving, $\theta$=27

8. Aug 12, 2011

### krautkramer

Re: Help !! How can I find acute Angle theta??

hey, what is this 'arccot'??How I can find the answer 27 degree?? by calculator or any other means...

9. Aug 12, 2011

### PeterO

Re: Help !! How can I find acute Angle theta??

Are you allowed to use a calculator when you do this question?

10. Aug 12, 2011

### krautkramer

Re: Help !! How can I find acute Angle theta??

Yes of course...You are right and the answer is 27 dgree..it was simple for you...But for me,it is a herculian task...still I don't know how to find it by using windows scientific calculator

11. Aug 12, 2011

### krautkramer

Re: Help !! How can I find acute Angle theta??

Yes of course...I think so...Otherwise no one will pass the final exam...

12. Aug 12, 2011

### PeterO

Re: Help !! How can I find acute Angle theta??

Try the following:

Write down an angle - eg 17
Take tan 17
use 1/x, the reciprocal, on the answers
now do inverse tan and write down that answer.

repeat starting with an angle different to 17 degrees.

Note anything?

13. Aug 12, 2011

### PeterO

Re: Help !! How can I find acute Angle theta??

In that case, try each of the options in the cot function.

If your calculator doesn't have a cot function, use the tan function followed by the 1/x function.

Last edited: Aug 12, 2011
14. Aug 12, 2011

### krautkramer

Re: Help !! How can I find acute Angle theta??

Hoooorahhh, Got it..Today,I learned lot of mactamactics...Thanks and 1000 hugs to sonic generation and other friends....My examination body should allow us to use internet during exam.

Determine the acute angle θ when tan 63° = cot θ.

Tan63° =Cot θ
Ie, 1.96261= Cot θ

Arccot(1.96261)=Cot θ

Ie, Cot θ=1.96261

Tan θ=1/1.96262

So, θ=Tan-1(1/1.96262)

Ans=27°

15. Aug 12, 2011

### PeterO

Re: Help !! How can I find acute Angle theta??

The information / expression you were really holding out for - and we were holding back on is

Tan θ = Cot (90 - θ) or Cot θ = tan (90 - θ)

Similarly

Sin θ = Cos (90 - θ) or Cos θ = Sin (90 - θ)

so Tan 63 = Cot (90 - 63) = Cot 27

That is the complementary angle stuff I was trying to lead you to.

16. Aug 12, 2011

### asmani

Re: Help !! How can I find acute Angle theta??

Notice that tan(θ)=cot(90-θ) for any θ.

17. Aug 12, 2011

### HallsofIvy

Staff Emeritus
Re: Help !! How can I find acute Angle theta??

This was posted in both "Precalculus Homework" and "General Mathematics" so I am merging the two threads.