At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
hello, its been a long time since ive done trigonometry, can you please help me?
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)?
for what angles do sin and cos equal each other?
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]?
values of x go from 0 to 2pi
Exactly. Now, are you allowed to use a grapher on this one? Do you know your unit circle?
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
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.
That's a circle divided into quarters.
Oops, I meant 0, 2pi, sorry.
yeah i drew it out
Sorry about that. Alright, so when you drew that out, you noticed that pi/4 and 5pi/4 are both right, correct?
Both of those have x and y values that are equal.
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.
essentially, cos(pi/4) = sin(pi/4) and cos(5pi/4) = sin(5pi/4).
now, how can we make the degree (3x) equal pi/4 and 5pi/4?
We want 3x = pi/4 and 3x = 5pi/4, can you solve both of those problems algebraically?
Once you do, you have your answers. I hope I wasn't too confusing.
no problem, i understood everything, thanks!