What is this kind of question called, and how do I solve it?
I am just starting complex numbers (self-taught), and i am having trouble with the polar co-ordinates because of my incompetence with these questions.
When do the graph of sine and cosine cross each other?
>>7971755
I dont know. I can estimate it with graphs, but I dont know how to calculate it.
unless im just forgetting something really basic like an idiot...
>>7971740
[eqn]\sin \theta = \cos \theta[/eqn]
[eqn]\sin \theta = \sqrt{1-\sin^2\theta}[/eqn]
[eqn]2\sin^2 \theta = 1[/eqn]
[eqn]\sin \theta = \pm \frac{1}{\sqrt{2}}[/eqn]
Moral of the story, substitute either sin or cos and solve for the trig function.
>>7971755
no wait, i remember. when theta = 45°
>>7971759
>forgetting something really basic
It helps to keep the unit circle in mind.
>>7971764
Not just there. Remember you want to find the angles where points on the unit circle have the same x coordinate (cosine) and y coordinate (sine.) That means you want the points where the line y=x intersects the unit circle. These give the angles 45 deg and 225 deg for two, but you have to account for EVERY angle that gives these points, meaning 405 deg, 585 deg, -135 deg, etc. So you write 45+180k degrees where k is an integer (all solution angles are 180 deg apart on the circle)
Also, use radians, they will make things easier on you.
This won't be a nice clean number, you know?
Just off the top of my head, one of the solutions is between 0 and pi/4 tho
>>7971980
thats a 0 not a theta
confused me as well
>>7971996
Oh shit lol, OP, you're a dumbass
Well fuck me, I don't know what I was expecting.
Just say sinx=cosx, then think about it analytically.
What angle has the same x and y value on the unit circle?
k*pi+pi/4, where k = integer
There we go, took me way too long.
I wanted a way to prove it.
>>7971740
Use the trig identity sin^2 (x) + cos^2 = 1
You should be able to do this
I'm assuming that is a 0,not a theta though
>>7971980
Yes, it will be.
It has a very simple closed form. In fact, you can write all of the (infinite number of) solutions in a single expression.
>>7972203
My bad, I thought the 0 was a theta
>>7972060
K=int. That's cute. We mathematicians use [math]K \in \Bbb N[/math]
>>7972217
> ivory tower
Sci is fucking retarded sometimes. Divide everything by cos. Then it's tan - 1 = 0. Solve from there.
>>7972217
Using the natural number set is wrong...
>>7972060
>int
ban the underage highschooler
