anonymous
  • anonymous
Solve the following equation, giving the exact solutions which lie in [0, 2π). (Enter your answers as a comma-separated list.) sin(2x) = sin(x)
Mathematics
katieb
  • katieb
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DeoxNA
  • DeoxNA
There's a pythagorean identity that says: sin(2x)=2*sin(x)*cos(x). so... 2cos(x)=1 cos(x)=1/2 And here's when your trig flashcards come in handy...
anonymous
  • anonymous
for some reason... i'm getting x = 0, pi/3/5pi/3 as the answers
anonymous
  • anonymous
im i wrong?

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DeoxNA
  • DeoxNA
No, you're right, I'm wrong. Doing it graphically I do get your answers. That's odd...let me think...
anonymous
  • anonymous
but when i plug them in the program says I'm wrong
DeoxNA
  • DeoxNA
Your's or mine?
anonymous
  • anonymous
mine. because there is a box that says x=
anonymous
  • anonymous
NO...you get \[x=0, \frac{ \pi }{ 3 }, \pi, \frac{ 5\pi }{ 6 }, 2\pi\]
anonymous
  • anonymous
@DeoxNA erased a solution.
anonymous
  • anonymous
by dividing \[\sin\theta\], you erase values. that's the worst mistake you can do in these questions.
anonymous
  • anonymous
oh i see
anonymous
  • anonymous
\[\sin(2x)-\sin(x)=0\] \[2\sin(x)\cos(x)-\sin(x)=0\] \[\sin(x)(2\cos(x)-1)=0\]
anonymous
  • anonymous
\[\sin(x)=0\] or \[\cos(x)=\frac{ 1 }{ 2 }\]
anonymous
  • anonymous
Hey Asteck can I ask you another question or DeoxNa
DeoxNA
  • DeoxNA
Yeah I was thinking about that, like when you get holes in the graph when you simplify rational functions...Well thank you @Azteck .
DeoxNA
  • DeoxNA
@dainel40 Sure thing...
anonymous
  • anonymous
Given the information below, find the exact values of the remaining circular functions of θ. sec(θ) = 10 with θ in Quadrant IV I got Sine= -sqrt(99)/10 Cos= 1/10 But I can't get Tangent... I tried doing Sine/Cos but I get the wrong answer
anonymous
  • anonymous
To get tangent... shouldnt i do sine/cos?
DeoxNA
  • DeoxNA
I'm sorry, but I don't really get what you're doing. Are you trying to convert the secant to the other circular functions? Or do you replace the secant with each respective function?
anonymous
  • anonymous
im just trying to get Tangent ... I already know what sine and cos are
DeoxNA
  • DeoxNA
The tangent of what?
anonymous
  • anonymous
Given the information below, find the exact values of the remaining circular functions of θ. sec(θ) = 10 with θ in Quadrant IV I got Sine= -sqrt(99)/10 Cos= 1/10 But I can't get Tangent... I tried doing Sine/Cos but I get the wrong answer
anonymous
  • anonymous
Like I already know Sine and Cosine,.. Idk how to get Tangent
DeoxNA
  • DeoxNA
Ok, sorry I didn't get what you were saying at first....Somehow I got it this time, so if: sec(θ)=10 in Quadrant IV θ=4.8122 tan(4.8122)=-9.985. How did you get an exact theta?
anonymous
  • anonymous
It's -√99/10. sin^2 + cos^2 = 1 (1/10)^2 + sin^2 = 1 1/100 + sin^2 = 1 sin^2 = 99/100 sin = ± √ (99/100) = ± √99 / √100 = ± √99 / 10
DeoxNA
  • DeoxNA
Are you sure its not (√ 99/10)/(1/10)=√ 99 ? I know I'm not being much help, but its just that the answer makes perfect sense...

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