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dainel40

  • 2 years ago

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)

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  1. DeoxNA
    • 2 years ago
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    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...

  2. dainel40
    • 2 years ago
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    for some reason... i'm getting x = 0, pi/3/5pi/3 as the answers

  3. dainel40
    • 2 years ago
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    im i wrong?

  4. DeoxNA
    • 2 years ago
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    No, you're right, I'm wrong. Doing it graphically I do get your answers. That's odd...let me think...

  5. dainel40
    • 2 years ago
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    but when i plug them in the program says I'm wrong

  6. DeoxNA
    • 2 years ago
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    Your's or mine?

  7. dainel40
    • 2 years ago
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    mine. because there is a box that says x=

  8. Azteck
    • 2 years ago
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    NO...you get \[x=0, \frac{ \pi }{ 3 }, \pi, \frac{ 5\pi }{ 6 }, 2\pi\]

  9. Azteck
    • 2 years ago
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    @DeoxNA erased a solution.

  10. Azteck
    • 2 years ago
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    by dividing \[\sin\theta\], you erase values. that's the worst mistake you can do in these questions.

  11. dainel40
    • 2 years ago
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    oh i see

  12. Azteck
    • 2 years ago
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    \[\sin(2x)-\sin(x)=0\] \[2\sin(x)\cos(x)-\sin(x)=0\] \[\sin(x)(2\cos(x)-1)=0\]

  13. Azteck
    • 2 years ago
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    \[\sin(x)=0\] or \[\cos(x)=\frac{ 1 }{ 2 }\]

  14. dainel40
    • 2 years ago
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    Hey Asteck can I ask you another question or DeoxNa

  15. DeoxNA
    • 2 years ago
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    Yeah I was thinking about that, like when you get holes in the graph when you simplify rational functions...Well thank you @Azteck .

  16. DeoxNA
    • 2 years ago
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    @dainel40 Sure thing...

  17. dainel40
    • 2 years ago
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    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

  18. dainel40
    • 2 years ago
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    To get tangent... shouldnt i do sine/cos?

  19. DeoxNA
    • 2 years ago
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    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?

  20. dainel40
    • 2 years ago
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    im just trying to get Tangent ... I already know what sine and cos are

  21. DeoxNA
    • 2 years ago
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    The tangent of what?

  22. dainel40
    • 2 years ago
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    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

  23. dainel40
    • 2 years ago
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    Like I already know Sine and Cosine,.. Idk how to get Tangent

  24. DeoxNA
    • 2 years ago
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    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?

  25. dainel40
    • 2 years ago
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    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

  26. DeoxNA
    • 2 years ago
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    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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