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#1 2013-12-09 18:17:38

steveyi
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Need help on these 4 TRIG problems

Actually just one question

3. If sin(θ)=−0.6878 and π≤θ≤3π/2, approximate the following to four decimal places.

(a) cos(θ) =  (Round to four decimal places.)
(b) tan(θ) =  (Round to four decimal places.)

It's looking for an answer to (a) and (b). Im completely confused on this problem , dont know what to do.

Last edited by steveyi (2013-12-09 19:04:28)

#2 2013-12-09 19:43:12

bob bundy
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Re: Need help on these 4 TRIG problems

hi steveyi

Welcome to the forum.

There are formulas connecting sin, cos and tan:



but, as you've got these decimal forms that means you'd have to use a calculator anyway so why not

(i) use a calc. to get theta

(ii) Your calc. will give a negative value so reverse the sign, then cos theta in the range 0 to pi/2

(ii) As you want a third quadrant value add another pi to your answer.

(iii) As tan is positive in the third the value your calc. gives will be the one.

http://www.mathsisfun.com/algebra/trig- … rants.html

Because trig functions are multi-valued and a calculator will only give one answer, you'll always have to do a bit of this to get the values in the right quadrant.

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

#3 2013-12-10 02:55:43

bobbym
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Re: Need help on these 4 TRIG problems

Hi;

Using the most famous trig identity known ( already given to you in post #1 ) you can get one answer right away.





round to 4 digits .7259

tan(x) you can do.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#4 2013-12-10 04:16:02

steveyi
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Re: Need help on these 4 TRIG problems

bobbym wrote:

Hi;

Using the most famous trig identity known ( already given to you in post #1 ) you can get one answer right away.





round to 4 digits .7259

tan(x) you can do.

The answer was wrong (.7259).

#5 2013-12-10 04:20:49

anonimnystefy
Real Member

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Re: Need help on these 4 TRIG problems

Try the negative answer, i.e., -0.725900241...


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#6 2013-12-10 04:26:26

bobbym
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Re: Need help on these 4 TRIG problems

Hi;

Yes, because of  π ≤ θ ≤ 3π/2.


From the graph you should try the negative of my answer.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#7 2013-12-10 06:17:09

bob bundy
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Re: Need help on these 4 TRIG problems

some careless poster wrote:

(ii) As you want a third quadrant value add another pi to your answer.

What was I talking about ?  Obviously you didn't want the angle, rather the cosine of the angle; so yes, please reverse the sign to get the third quadrant value.  Sorry.  shame  Please pretend I said this in post 2.

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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