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This will give you the set of solutions between 0 and 720, which are all integer multiples of ##\pi##.Therefore, in summary, to solve for sin(x)=0, you can use the general solution formula x=n\pi; n\in ℤ, which takes into account the periodicity of the sin function and gives all solutions between 0 and 720. Using the arcsin function will only give you one solution, 0, as it is restricted to a smaller domain.

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kontejnjer

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Mark44

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Using arcsin doesn't get you far. By common agreement, the arcsine function is the inverse of the Sin() function, which is the same as the sin() function, but with a domain restricted to ##[-\pi/2, \pi/2]##. This restriction makes Sin() a one-to-one function, therefore a function that has an inverse. The restricted domain of ##[-\pi/2, \pi/2]## for Sin is the range of its inverse, arcsin. Taking arcsin(0) will get you only one value; namely, 0.Scheuerf said:

To find all solutions of the equation sin(x) = 0 you have to understand the periodicity of the sin function and that its intercepts are all of the integer multiples of ##\pi##.

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Drafter

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Here is a the general formula of cosθ=1/2

I use the term "general formula" loosely since I do not know it's exact terminology, but anyways, here is cos(θ)=1/2.

The solution to this equation is any value of x that makes Sin(x) equal to 0. This includes 0 itself, as well as any multiple of π.

To solve this equation, you can use the inverse of the sine function, which is Arcsin. You would take the inverse sine of both sides of the equation, which would give you x=0 and x=π as solutions.

The sine function is a periodic function, meaning it repeats its values at regular intervals. In the case of Sin(x), the function repeats itself every 2π units. This means that there are infinitely many solutions to the equation Sin(x)=0, as the function will continue to repeat itself in both positive and negative directions.

The graphical representation of the solutions to Sin(x)=0 is a straight line passing through the x-axis at 0 and π. This is because the values of the sine function at these points are 0.

One real-life application of solving Sin(x)=0 is in physics or engineering, where the sine function is used to model the motion of a pendulum. In order to find the maximum and minimum angles of the pendulum, you would need to solve the equation Sin(x)=0 to find the values of x at these points.

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