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How do you solve 6sin x 1 plus 9sin x algebraically over the domain 0 x 2pi?
Wiki User
∙ 9y ago
6*sinx = 1 + 9*sinx => 3*sinx = -1 => sinx = -1/3
Let f(x) = sinx + 1/3
then the solution to sinx = -1/3 is the zero of f(x)
f'(x) = cosx
Using Newton-Raphson, the solutions are x = 3.4814 and 5.9480
It would have been simpler to solve it using trigonometry, but the question specified an algebraic solution.
Wiki User
∙ 9y ago
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A level 2009 oct nov questin flash out?
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What is calculus used for?
not muchLIAR. we do it in maths so ner ner ner ner ner.Up until calculus, you can essentially deal with functions of a constant slope (a straight line). I.e.: y = 1/3x + 9. We know the slope on that function is 1/3. However what is the slope of y = e5x+sin(9x)? It's y' = 5e5x+9cos(x)You should also know trigonometry and can use some trig functions to deviate from constant slopes, but you really don't know how to find the slopes. What is the slope of y = cos(9x)? It's y' = -9sin(9x)Calculus teaches you two fundamental operations (and a whole lot of application with these two operations):1) How to find the slope of a curve (the derivative)This let's you find the maximum and minimum's of a function, optimize problems (i.e., figure out how to use the least amount of materials given some parameters), and has and endless amounts of utility.and2) How to find the area under a curve. (the integral)This let's you find the totals for a number of problems (example, find the total accumulated amount of money, given a function that relates time and money), let's you calculate the real areas, volumes, etc. of realistic surfaces (not everything is shaped like a box or triangle), and also has endless amounts of utility.If you want to go into any science, engineering, research field, or just any technical field, you are going to want to have calculus. It is a fundamental subject, that teaches you operations (must like addition and subtraction), finding thedeterminateand integrals are too operations.
