anonymous
  • anonymous
Solve 1 = cot^2(x) = 8sinx, for 0(lesser-than-or-equal-to) x (lesser-than-or-equal-to) 360 degrees??
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
r u sure u have correct question? The two '=' signs?
anonymous
  • anonymous
sorry, 1+ cot^2.....
anonymous
  • anonymous
my bad. didn't press shift.

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anonymous
  • anonymous
ahh u could try replacing cot^2x with cosec^2x - 1 = 1/sin^2x + 1
anonymous
  • anonymous
but that would be 1 + coesc^2x - 1, which would be cosec^x.
anonymous
  • anonymous
hmm lets try this: 1 + ( 1 - sin^2x) = 8 sinx ---------- sin^2x sin^2x + 1 - sin^2x = 8 sin^3 x sin^3 x = 1/8 s in x = +/- 1/2
anonymous
  • anonymous
x = 30, 150, 210, 330 degrees
anonymous
  • anonymous
how did you get that?? \[1 + \cot^2x = 8sinx\] so \[cosec^2x = 8sinx\] now what??
anonymous
  • anonymous
cosec^2 x = 1 / sin^2 x
anonymous
  • anonymous
yes. so?
anonymous
  • anonymous
you replace cot^2x by cosec^2 x - 1 because cosec^2x = 1 + cot^ 2 x
anonymous
  • anonymous
but you can replace 1 = cot^2x by cosec^2x straight away!!
anonymous
  • anonymous
*1 + cot^2x
anonymous
  • anonymous
yea right - i didnt see the obvious! - but my method comes out with the same answer. your way is better though! they both come to 1 / sin^2x = 8 sinx cross multiply: 8 sin^3 x = 1 sin^3 x = 1/8 sin x = 1/2 or -1/2
anonymous
  • anonymous
ohhh. cool. i didn't know how to simplify it :P
anonymous
  • anonymous
but it can't be -0.5, though, can it??
anonymous
  • anonymous
hold on - sorry - i-m prone to error today the cube root of 1/8 is 1/2 only so x = 30, 150 only
anonymous
  • anonymous
i think tahs correct now lol!
anonymous
  • anonymous
it's okayy, i have these weird days too :P
anonymous
  • anonymous
can you help me with another question??
anonymous
  • anonymous
ok

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