Sinusoidal equations

with sinusoidal equations you have to use the circle chart that i posted. when a line passes the circle, it passes through two points of the circle which are the answers.

Why are you working in degrees and not radians? Also, arccos(0)=270 as well, so it would be 90+180n

Trig equations have infinitely many solutions. Do you mean that the domain of your answers is only the values on the chart you posted?

Add π rad to the solution?

That's just the way the problem was. Im doing khan academy

Can you post exactly what the problem asks? Better yet take a screen shot and post that

adding pi to 90 might work. the secons solution is supposed to be -9+36n

Just wait until you get to complex roots my nigga kek

what do you mean? The problem is 4cos(10x)+2=2. They ask for the solutions in degrees

i believe ive done that. quadratic equation right?

But what’s the domain of the answers? There’s infinitely many solutions to that problem but you keep talking about two.

Look up eulers equation

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I dont know exactly what you're talking about. The two answers are 9+36n and -9+36n. I want know how they got -9+36n.

The complex roots of any number are equidistant on a circle centered in the radius of the complex plane. Its similar to this sinuisoidal stuff. But i thinkt thats complex analysis (ie. real math). I swear one day I'll be good at math. And so good my age is irrelevant.

Wow. That's looks pretty difficult

Im working towards being good at math too

They get -9 because cos(0)= -90 as well. And I mean the domain as in what range of values are you looking at for x? All numbers? From -90 to 90? 0 to 1? Like I keep saying, there’s infinitely many solutions, which should be obvious from the “+36n” term in the solutions.

Yeah thanks. I wasnt asking about n

n has to be a natural number

I hope you understand my point about n and the true number of solutions though. It’s not enough to know how to solve it, you should hopefully understand what the solutions mean.

i think ive figured it out with out using the circle chart. you take pi and then take it away from 90.

I do. i think you were saying that n is a variable.

Yeah, but it's important to realise that n is an arbitrary variable, a bit like c when you integrate equations. No matter the value of n (as long as it is an integer), the result of your first equation will always be the same as it's a cosine function and it always loops.

n can be any real integer. We can't tell what the valueof n is from the starting equation, hence we just assume that there is a number that gets multiplied by n.

ok. i see

>real integer
Cmon man

A function is defined in part by its domain (the set of input values). For instance y = x defined for all real numbers and then only on the interval [0, 1]. These are technically two different functions; both are straight lines with slope 1, and y intercept 0, but one of course extends infinitely in the 2d plane while the other is limited to a small segment