0

# sine/cosine=tangens, equation help.

Sun 19 May, 2013 06:53 pm
That's simple enough. But then the next equation pops up, and it goes like this:

sin^2 x -3 sin x * cos x + 2 cos^2 x = 0 , x between [-pi , pi]

I'm following a text book, and in the examples of how to solve this, by dividing sine with cosine, all of them had the same exponents. In this equation there are some in the first power and some in the second. I have the sneaking suspicion that this is rather simple, but I am stuck in my own thoughts, and could use some help.
• Topic Stats
• Top Replies
Type: Question • Score: 0 • Views: 668 • Replies: 6
No top replies

Kolyo

1
Sun 19 May, 2013 07:14 pm
@Cyracuz,
Fortunately each of your terms is one trig function multiplied by another. The first term is sin*sin; the second is sin*cos; the third is cos*cos. If you divide everything by cos^2 x and then substitute u for tan(x), you can then solve the resulting quadratic equation for u.
Cyracuz

1
Sun 19 May, 2013 07:29 pm
@Kolyo,
That sounds like just the thing. It didn't occur to me to think of "sin^2" as one term. Thanks. If this thread dies here, take it as a good sign.
0 Replies

Cyracuz

1
Sun 19 May, 2013 07:56 pm
Great success. I was able to solve it with all 4 solutions to x. Thanks.

Took some time to figure it out though, when my calculator gave me the answer 0.7853.... instead of pi/4.
markr

1
Sun 19 May, 2013 10:03 pm
@Cyracuz,
Or factor the original polynomial:

(sinx-2cosx)(sinx-cosx) = 0
sinx = 2cosx ==> tanx = 2
sinx = cosx ==> tanx = 1
Cyracuz

1
Mon 20 May, 2013 02:56 am
@markr,
At the moment I do not see how you did that. I see that the answers you arrived at are the right ones.
engineer

1
Mon 20 May, 2013 07:09 am
@Cyracuz,
I would have used Mark's approach also although I like the elegance of Kolyo's method.

Quote:
sin^2 x -3 sin x * cos x + 2 cos^2 x = 0

Let A = sin X and B = cos X then you get A^2 - 3AB + 2B^2 = 0 which factors to (A-B)(A-2B) = 0.
0 Replies

### Related Topics

Amount of Time - Question by Randy Dandy
logical number sequence riddle - Question by feather
Calc help needed - Question by mjborowsky
HELP! The Product and Quotient Rules - Question by charsha
STRAIGHT LINES - Question by iqrasarguru
Possible Proof of the ABC Conjecture - Discussion by oralloy
Help with a simple math problem? - Question by Anonymous1234567890
How do I do this on a ti 84 calculator? - Question by Anonymous1234567890

1. Forums
2. » sine/cosine=tangens, equation help.