Solve for x sin(x)+1=0

Problem

sin(x)+1=0

Solution

1. Isolate the trigonometric term by subtracting 1 from both sides of the equation.

sin(x)=−1

2. Identify the values of x on the unit circle where the sine function (the y-coordinate) is equal to −1

x=(3*π)/2

3. Generalize the solution to include all possible angles by adding integer multiples of the period 2*π

x=(3*π)/2+2*π*n

4. Specify that n represents any integer.

n∈ℤ

Final Answer

sin(x)+1=0⇒x=(3*π)/2+2*π*n,n∈ℤ

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