SOLUTION: Solve the system: {{{system(r*sin(theta)=3, r=4(1+sin(theta)))}}}

Algebra ->  Trigonometry-basics -> SOLUTION: Solve the system: {{{system(r*sin(theta)=3, r=4(1+sin(theta)))}}}      Log On


   

Question 1121000: Solve the system: system%28r%2Asin%28theta%29=3%2C+r=4%281%2Bsin%28theta%29%29%29
Found 2 solutions by Edwin McCravy, mccravyedwin:
Answer by Edwin McCravy(20067) About Me  (Show Source):
You can put this solution on YOUR website!
Solve the system: system%28r%2Asin%28theta%29=3%2C+r=4%281%2Bsin%28theta%29%5E%22%22%29%29

Substitute the value of r from the second equation in the first equation:

r%2Asin%28theta%29=3

4%281%2Bsin%28theta%29%5E%22%22%29%2Asin%28theta%29=3

4%2Asin%28theta%29%2A%281%2Bsin%28theta%29%5E%22%22%29=3

4%2Asin%5E%22%22%28theta%29%2B4sin%5E2%28theta%29%5E%22%22=3

4%2Asin%5E%22%22%28theta%29%2B4sin%5E2%28theta%29%5E%22%22-3=0

Swap the first two terms:

4sin%5E2%28theta%29%5E%22%22%2B4%2Asin%5E%22%22%28theta%29-3=0

Factor the left side:

%282sin%28theta%29%2B3%5E%22%22%29%282sin%28theta%29-1%5E%22%22%29=0

2sin%28theta%29%2B3=0,   2sin%28theta%29-1=0
2sin%28theta%29=-3,   2sin%28theta%29=1  
cross%28sin%28theta%29=-3%2F2%29,   sin%28theta%29=1%2F2

All sines are between -1 and +1 so -3/2 is not a possibility,
so we ignore the left equation.

sin%28theta%29=1%2F2

theta=matrix%281%2C3%2C30%5Eo%2B360%5Eo%2An%2Cor%2C150%5Eo%2B360%5Eo%2An%29, if θ is in degrees. 

or

theta=matrix%281%2C3%2Cpi%2F6%2B2pi%2An%2Cor%2C5pi%2F6%2B2pi%2An%29, if θ is in radians. 

Substituting in the first given equation:

r%2Asin%28theta%29=3
r%2A%281%2F2%29=3
expr%281%2F2%29r=3
r=6

Edwin

Answer by mccravyedwin(411) About Me  (Show Source):
You can put this solution on YOUR website!
This is a problem I solved many years ago, maybe 10 years ago. I am using it to
inform you tutors about some history of this site. 

I picked a random date, October 16, 2020. At present the posts that you see on
the problem page were posted 4.5 years ago on October 16, 2020 are these:

1167408 (2020-10-16 05:27:24)
1167440 (2020-10-16 11:36:06)
1167453 (2020-10-16 13:36:10)
1167480 (2020-10-16 21:39:15)

Notice that the earliest one of those posted on that date at 5:27 AM was
numbered 1167408, and the last one posted on that date at 9:39 PM was numbered
1167480.

That means that on that date between 5:27 AM and 9:39PM there were 73 problems
posted. Can you believe?  I can because I remember.  Most of the 73 problems
posted on that date were solved by the many tutors who were around back then.
The posted problems that are still there now are the ones that the tutors back
then either didn't get to or weren't as interesting as the ones the tutors chose
to solve -- before they scrolled off.

I've been here since this site first opened way back in the early 2000's.  This
site was really hopping back then. I have seen many tutors come and go.

Now compare the fact that there were 73+ problems posted on October 16, 2020 to
the fact that 0 have been posted in the last few days!  Only the ads are keeping
this site going.  Perhaps some students are using this site as a source for
problems.  I don't know, but I fear this site is dying and is almost dead.    

Since I've been here from the start, I'm just informing you about this site in
case you haven't figured out what's going on.  
 
Cheers, Edwin