Math Is Fun Forum
  Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

You are not logged in.

#1 2013-12-08 19:17:38

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

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

Offline

#2 2013-12-08 20:43:12

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,393

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

Offline

#3 2013-12-09 03:55:43

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,676

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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Offline

#4 2013-12-09 05:16:02

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

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).

Offline

#5 2013-12-09 05:20:49

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,525

Re: Need help on these 4 TRIG problems

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


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

Offline

#6 2013-12-09 05:26:26

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,676

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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Offline

#7 2013-12-09 07:17:09

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,393

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

Offline

Board footer

Powered by FluxBB