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anonymous

  • 5 years ago

sin(3x)=cos(3x) where x is defined to be in the interval [0,2pi]

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  1. anonymous
    • 5 years ago
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    Hello

  2. anonymous
    • 5 years ago
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    hello, its been a long time since ive done trigonometry, can you please help me?

  3. anonymous
    • 5 years ago
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    Yes. First off, can you tell me in plain English what they are asking of you? Let's break it down: What are they asking for when they say sin(3x) = cos(3x)?

  4. anonymous
    • 5 years ago
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    for what angles do sin and cos equal each other?

  5. anonymous
    • 5 years ago
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    Great, yes, that is exactly right. For what value of X does cos(3x) and sin(3x) equal each other. Good. Now, what are they saying when they include: x is defined to be in the interval [0,2pi]?

  6. anonymous
    • 5 years ago
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    values of x go from 0 to 2pi

  7. anonymous
    • 5 years ago
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    Exactly. Now, are you allowed to use a grapher on this one? Do you know your unit circle?

  8. anonymous
    • 5 years ago
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    no im not allowed to use a graphing calculator, but i do remember the unit circle and after looking it up i can see that sin(pi/4)=cos(pi/4) but i know that pi/4 isnt the only answer, i just dont remember how to find the rest

  9. anonymous
    • 5 years ago
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    Alright, can you draw and label a unit circle for me? Just draw it out on paper. A quick sketch. Draw pi/2, pi, 3pi/4, and 0, pi.

  10. anonymous
    • 5 years ago
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    That's a circle divided into quarters.

  11. anonymous
    • 5 years ago
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    Oops, I meant 0, 2pi, sorry.

  12. anonymous
    • 5 years ago
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    yeah i drew it out

  13. anonymous
    • 5 years ago
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    Sorry about that. Alright, so when you drew that out, you noticed that pi/4 and 5pi/4 are both right, correct?

  14. anonymous
    • 5 years ago
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    Both of those have x and y values that are equal.

  15. anonymous
    • 5 years ago
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    We are trying to find all values of x where cos(3x)=sin(3x). We know for this to be true, the degree of cos and sin both have to equal pi/4 or 5pi/4.

  16. anonymous
    • 5 years ago
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    essentially, cos(pi/4) = sin(pi/4) and cos(5pi/4) = sin(5pi/4).

  17. anonymous
    • 5 years ago
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    now, how can we make the degree (3x) equal pi/4 and 5pi/4?

  18. anonymous
    • 5 years ago
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    We want 3x = pi/4 and 3x = 5pi/4, can you solve both of those problems algebraically?

  19. anonymous
    • 5 years ago
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    Once you do, you have your answers. I hope I wasn't too confusing.

  20. anonymous
    • 5 years ago
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    no problem, i understood everything, thanks!

  21. anonymous
    • 5 years ago
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    Great :D

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