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**steveyi****Member**- Registered: 2013-12-08
- Posts: 2

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 (2013-12-08 20:04:28)*

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 7,588

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

Children are not defined by school ...........The Fonz

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 104,380

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.****If it ain't broke, fix it until it is.** **A number by itself is useful, but it is far more useful to know how accurate or certain that number is.**

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**steveyi****Member**- Registered: 2013-12-08
- Posts: 2

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).

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,015

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 104,380

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.****If it ain't broke, fix it until it is.** **A number by itself is useful, but it is far more useful to know how accurate or certain that number is.**

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 7,588

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. Please pretend I said this in post 2.

Bob

Children are not defined by school ...........The Fonz

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

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