anonymous
  • anonymous
solve the equation on the interval 0≤x≤2pi tanx=0
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
Erin have you tried solving this yourself? I encourage you to learn from the solutions I provided and try and solve this yourself first. If you get stuck, then feel free to ask.
anonymous
  • anonymous
thank you, i'm a bit confused but i'll try solving it myself
anonymous
  • anonymous
One hint is that tan(x) = sin(x) / cos(x) and the saying tan(x) = 0 is the same as saying sin(x) = 0. @erin512

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anonymous
  • anonymous
thanks again, ill try that could you maybe give me an explanation of just one more to help me understand and ill do the next one on my own? i'd really appreciate it
anonymous
  • anonymous
Remember what I said. tan(x) = 0 is the same as finding x for sin(x) = 0. This is because tan(x) = sin(x) / cos(x). Since tangent is the quotient of sine and cosine, and we are finding the values of x for where it's 0, we are really finding when the quotient sin(x) / cos(x) is 0. The quotient is 0 when sin(x) is 0 because when the numerator is 0, the whole fraction is 0. Where is sin(x) = 0 ? Look at the sine graph if you need to.
anonymous
  • anonymous
@erin512
anonymous
  • anonymous
tanx = 0 ---> x = n pie
anonymous
  • anonymous
Since the intervel is 0≤x≤2pi n = 0,1,2
anonymous
  • anonymous
n can equal any number?
anonymous
  • anonymous
oh nevermind thank you
anonymous
  • anonymous
Welcome
anonymous
  • anonymous
Generally, when tanx = a, x = { arctan(a) + k*pi, when k is whole }
anonymous
  • anonymous
so x = 1, 2?
anonymous
  • anonymous
i mean x=0,1,2
anonymous
  • anonymous
\[0 \le x \le 2\pi \] take tan on all \[\tan 0 \le \tan x \le \tan 2\pi\] => \[0 \le tanx \le 0 \] that means tanx =0 \[\ x=tan^{-1} 0= 0 = 2pi \]

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