Question

Help with simplifying trig expressions pls

Answer 1

\[\frac{ 2-\tan \theta }{ 2 \csc \theta - se \theta }\]

Answer 2

so far i got
\[\frac{ 2-(\sin \theta/\cos \theta )}{ 2(1/\sin \theta)-(1/\cos \theta) }\]

Answer 3

by changing it to sin and cos

Answer 4

that's cool. How about temporarily ignoring the numerator of your expression, finding the LCD of the denominator, and combining the 2 terms in the den. to 1 term?

Answer 5

would the lcd be sincos?

Answer 6

Yes, tho' I'd be a lot happier if you'd please write it as sin x cos x. Both functions sin and cos always have an argument (x).

Answer 7

so the denominator would be
\[2-(1/\sin \theta \cos \theta)\]

Answer 8

or did i combine it wrong

Answer 9

Not quite. That 2 must have the same denominator, sin x cos x.

Answer 10

So far, your original denom has 2 terms. The first one is 2/sin x.

Mult. both the 2 and the sin x by cos x. Your result?

Answer 11

2 cos x sin x cos x?

Answer 12

that first term of the denom. of your original fraction is \[\frac{ 2 }{ \sin x }\]

Answer 13

mult. both the numerator (2) and the denom. (sin x) by cos x, please.

Answer 14

\[ \frac{ 2\cos \theta}{ \sin \theta \cos \theta}\]

Answer 15

very good. hold that. look at the 2nd term in the denom. It's 1/cos x. Mult. both numerator and denom of this 1/cos x by sin x.

Answer 16

\[\frac{ \sin \theta }{ \cos \theta \sin \theta }\]

Answer 17

Great. Now, both of your fractions from the denom. have the LCD sin x cos x.
Combine these 2 fractions into 1fraction.

Answer 18

\[\frac{ 2 \cos \theta - \sin \theta }{ \sin \theta \cos \theta}\]

Answer 19

cool, cool. Now hold that whole result. Now focus on the numerator. What result did we obtain earlier?

Answer 20

um
\[2-(\sin \theta/\cos \theta)\]

Answer 21

But we mult. the 2 by (cos x / cos x) and thus got [(2cos x) -sin x] / cos x. Agree or not?

Your next task is to reduce your re-written fraction. Hint: the cos x cancels out.

Answer 22

i thought that was just in the denominator

Answer 23

Sorry, I know this is confusing. Remember, I asked you to hold the denominator of your fraction after we had modified it?

Answer 24

yes

Answer 25

somehow you'll have to find the final versions of our modified numerator and modified denominator, and then look for a way to cancel certain factors. My result comes out to simply sin x. You should go thru the steps necessary to obtain the same result.

Answer 26

ok one sec let me just redo the steps to groudn myself again srry

Answer 27

wait?
\[2 (1/\sin \theta) = 2/\sin \theta\]

Answer 28

You obtained the following yourself:\[\frac{ 2-(\sin \theta/\cos \theta )}{ 2(1/\sin \theta)-(1/\cos \theta) }\]

Answer 29

yea im just confused on the denominator

Answer 30

In the numerator the LCD is cos x. Before you can comebine the 2 terms in the numerator you MUST manipulate that '2' so that this term has denominator cos x also.
In the den. the LCD is sin x cos x.

Answer 31

Take a few moments to review what we've done. All the necessary work has been completed. We just need to put it together and to reduce the resulting fraction as much as possible.

Answer 32

oh ok so the numertaor is
\[\frac{ 2\cos - \sin \theta }{ \cos \theta }\]

Answer 33

http://sketchtoy.com/66986155

Answer 34

YES> Excellent. Hold that. Draw a red circle around it. Then focus on the denom. (making sure that your LCD is sin x cos x).

Answer 35

ok

Answer 36

wow. That was fast! Did you actually prepare that presentation on that other web site?

Any further questions about this problem?

Answer 37

Yep, I did.

Answer 38

looking over it

Answer 39

wow changing it in to x and y is really easy on the eyes :O

Answer 40

Surely saves a lot of typing as well.

Satisfied with our discussion? Question answered to your satisfaction?

Answer 41

yea ty so much for sticking with me this long :D

Answer 42

Happy to do it; you know your stuff, which makes it a pleasure to work with you. Thx for the medal!

Answer 43

:D