+267 How would I solve an equation like this? Taking the arcsine of both sides doesn't lead me to anywhere that'd be benefitial.
I understand that there's and infinite amount of answers but for example what if I wanted all the solutions between 0 and 2pi? How would I go about solving something like this where I can't seem to pull out an x.
Cheers and thanks in advance.
+33616 There are 3 solutions. One is obvious from the graph below. The other two can be found numerically (one way is to guess, using the graph as a starting point, and then refine your guess until you get as close as you want).
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+267 Silly me I'm not sure why I thought there'd be an infinite amount of solutions. I thought that taking the arcsine would add a period of 360 degrees to the answer I suppose. Thank you. Is there a way to solve this algebraically? And an additional question for sinx = 1 - x/pi. Can I solve that algebraically? I imagine it'd be mire difficult..
+33616 You cannot obtain an explicit algebraic solution in the form x = something here, where the 'something' is independent of x.
A possible numerical approach is to use the Newton-Raphson method, where you have to subtract one side from the other to create a function that is equal to zero:
The positive solution here is x = 2.314. The negative solution could be obtained by using an initial guess of, say -3, though the symmetry here makes it obvious that the negative solution is x = -2.314.
You would need to use a similar numerical method for your other suggestion.
Here one obvious solution is x = pi. Use Newton-Raphson to find the others. For example:
So another solution is x = 0.828 (and because of the sine curve, the final solution is at x = 2pi - 0.828).
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