Problem

How many solutions of the following equation exist on the interval [0,2π) ? sin⁡(7x)=0

Answer

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Answer

So, there are 14 solutions to the equation sin⁡(7x)=0 in the interval [0,2π).

Steps

Step 1 ：The solutions to the equation sin⁡(7x)=0 are given by 7x=nπ, where n is an integer.

Step 2 ：To find the number of solutions in the interval [0,2π), we need to find the number of integers n such that 0≤7x<14π. This means 0≤n<14.

Step 3 ：The solutions are 0,0.44879895,0.8975979,1.34639685,1.7951958,2.24399475,2.6927937,3.14159265,3.5903916,4.03919055,4.48798951,4.93678846,5.38558741,5.83438636

Step 4 ：So, there are 14 solutions to the equation sin⁡(7x)=0 in the interval [0,2π).

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