# RESPONSE to PreCalc Question

posted by .

h t t p : / / w w w . j i s k h a . c o m / d i s p l a y . c g i ? i d = 1 2 6 7 4 1 7 1 8 8

¡î3sinx + cosx = 1
¡î3cosx = 1-cosx
square both sides
3cos^2 x = 1 - 2cosx + cos^2 x
3(1-sin^2 x) = 1 - 2cosx + cos^2 x
this reduces easily to
2cos^2 x - cosx - 1 = 0
(2cosx + 1)(cosx - 1) = 0
cosx = -1/2 or cosx = 1
x or theta = 120¨¬ , 240¨¬ or 0 , 360¨¬
x = 0, 2pi/3, 4pi/3, 2pi

Line 2 you subtracted cos x form both sides

¡î3sinx + cosx = 1
¡î3cosx = 1-cosx
how did the sin x next to the SQRT(3) change to cos x magically...

I don't think I'm seeing something here that I should be...

• RESPONSE to PreCalc Question -

Here's what I did

SQRT(3)sinx + cosx = 1

subtract cos x from both sides

SQRT(3)sinx = 1 - cosx

squared both sides

3 sin^2 x = 1 - 2cosx +cos^2 x

replaced sin^2 x with a trig idendity

3 (1 - cos^2 x) = 1 - 2cosx + cos^2 x

multiplied out the three

3 - 3cos^2 x = 1 - 2cosx + cos^2 x

subtracted cos^2 x from both sides

3 - 4cos^2 x = 1 - 2cosx

3 - 4cos^2 x + 2 cosx = 1

subtracted 1 from both sides

2 - 4cos^2 x + 2cosx = 0

factored out the 2

2( 1 - 2cos^2 x + cos x) = 0

factored out the cosx

2(1 +cosx(-2cosx + 1) = 0

2 = 0 or 1 +cosx(-2cosx + 1)=0

from which I am stuck yet again...

• sorry Kate RESPONSE to PreCalc Question -

Sorry Kate, I had written it out on paper and when I copied it to type I must have "jumped" lines.

Here is the good version:
√3sinx + cosx = 1
√3sinx = 1 - cosx
square both sides
3sin^2 x = 1 - 2cosx + cos^2 x
3(1 - cos^2 x) = 1 - 2cosx + cos^2 x
3 - 3cos^2 x = 1 - 2cosx + cos^2 x
-4cos^2 x + 2cosx + 2 =0
2cos^2 x - cosx - 1 = 0

Notice I had that, so the rest of my post is ok

I also included another reply to your first posting below suggesting the method your text is probably using.

• RESPONSE -

Thanks i got to read that post...
but now that I got to this I don't see what is wrong with doing it this way but i guess it is important to solve both ways

heres what I did
-4cos^2 x + 2cosx + 2 =0
factored
(-4cosx - 2)(cosx - 1) = 0

-4cosx - 2 = 0 or cosx - 1 = 0

-4cosx - 2 = 0
-4cosx = 2
divided by -4 on both sides
cosx = -1/2
(2 pi)/3, (4 pi)/3

cosx - 1 = 0
cosx = 0
x = 0

solutions
x = 0, (2 pi)/3, (4 pi)/3

now I checked my solutions with my magic number box (calculator) and oddly enough the third solution, (4 pi)/3, does not work but yet the other ones do...

I do not see why???
Well of to figuring out that other way...

I just don't understand what is wrong with the third solution and this way of solving is much easier I but I guess I got figure out the other way as well

THANKS

• RESPONSE to PreCalc Question -

I explained why the second answer of 4pi/3 does not work in the reply to your first posting below

When you square both sides of an equation, extraneous roots are sometimes introduced. That is why all answers must be checked in the original equation, which is what I showed you and did.

0, 2pi/3, 2pi (0, 120 degrees, 360 degrees)

• RESPONSE to PreCalc Question -

THANKS

## Similar Questions

1. ### Physiology

Which one(s) of the essetional chemcial elements (C, H, O, N) does blood contain. You only need to ask the question once. Additional repetitions will not get you a faster response. An answer to your question can be found in response …
2. ### Geometry

I HAVE A QUESTION. When I post a question and there is now response to it does it means that my answer to my questions are correct?
3. ### English expression

What is the suitable response to the greeting, 'Hi.'?
4. ### French

What's wrong with my response in this: Question: À qui aimes-tu rendre visite?
5. ### French response

Mathmate, I wrote a response below. The worksheet I worked on was a crossword puzzle and question 18 is only a five letter word and i'm not sure what it may be.
6. ### PHY: To AJAYB, follow up on previous response

First, I'd like to thank you for your response to my question. However, I had some follow up questions on your response from Saturday, July 28, 2012 at 8:27am. If you could take a look at that post and get back to me, it would be greatly …
7. ### AP CALCULUS

I have my test tomorrow. I am very weak at free response. What kind of question they ask in free response?
8. ### precalc

This question is from the previous question. What was the change in distance in miles?
9. ### Beginners Spanish

I need to form a question out of this response. I wanted to know if it was correct. Response:Hay mucha tarea hoy. Question I formed:¿Cuánta tarea hay hoy?
10. ### Reiny

Just a question for you. How do you remember all this. I'm wondering because I'm in precalc and I always seem to forget how to do the problems a couple weeks after the test. You seem to know everything without even hesitating. Side …

More Similar Questions