Question

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

Answer 1

Hello

Answer 2

hello, its been a long time since ive done trigonometry, can you please help me?

Answer 3

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)?

Answer 4

for what angles do sin and cos equal each other?

Answer 5

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]?

Answer 6

values of x go from 0 to 2pi

Answer 7

Exactly.

Now, are you allowed to use a grapher on this one? Do you know your unit circle?

Answer 8

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

Answer 9

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.

Answer 10

That's a circle divided into quarters.

Answer 11

Oops, I meant 0, 2pi, sorry.

Answer 12

yeah i drew it out

Answer 13

Sorry about that.

Alright, so when you drew that out, you noticed that pi/4 and 5pi/4 are both right, correct?

Answer 14

Both of those have x and y values that are equal.

Answer 15

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.

Answer 16

essentially, cos(pi/4) = sin(pi/4) and cos(5pi/4) = sin(5pi/4).

Answer 17

now, how can we make the degree (3x) equal pi/4 and 5pi/4?

Answer 18

We want 3x = pi/4 and 3x = 5pi/4, can you solve both of those problems algebraically?

Answer 19

Once you do, you have your answers. I hope I wasn't too confusing.

Answer 20

no problem, i understood everything, thanks!

Answer 21

Great :D