anonymous
  • anonymous
sin(3x)=cos(3x) where x is defined to be in the interval [0,2pi]
Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
Hello
anonymous
  • anonymous
hello, its been a long time since ive done trigonometry, can you please help me?
anonymous
  • anonymous
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)?

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anonymous
  • anonymous
for what angles do sin and cos equal each other?
anonymous
  • anonymous
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]?
anonymous
  • anonymous
values of x go from 0 to 2pi
anonymous
  • anonymous
Exactly. Now, are you allowed to use a grapher on this one? Do you know your unit circle?
anonymous
  • anonymous
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
anonymous
  • anonymous
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.
anonymous
  • anonymous
That's a circle divided into quarters.
anonymous
  • anonymous
Oops, I meant 0, 2pi, sorry.
anonymous
  • anonymous
yeah i drew it out
anonymous
  • anonymous
Sorry about that. Alright, so when you drew that out, you noticed that pi/4 and 5pi/4 are both right, correct?
anonymous
  • anonymous
Both of those have x and y values that are equal.
anonymous
  • anonymous
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.
anonymous
  • anonymous
essentially, cos(pi/4) = sin(pi/4) and cos(5pi/4) = sin(5pi/4).
anonymous
  • anonymous
now, how can we make the degree (3x) equal pi/4 and 5pi/4?
anonymous
  • anonymous
We want 3x = pi/4 and 3x = 5pi/4, can you solve both of those problems algebraically?
anonymous
  • anonymous
Once you do, you have your answers. I hope I wasn't too confusing.
anonymous
  • anonymous
no problem, i understood everything, thanks!
anonymous
  • anonymous
Great :D

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