Solve for x sin(x)=-4/5

Problem

sin(x)=−4/5

Solution

1. Identify the general solution for the sine function, which is given by x=arcsin(y)+2*n*π and x=π−arcsin(y)+2*n*π for any integer n

2. Calculate the principal value using the inverse sine function.

x=arcsin(−4/5)

3. Determine the approximate numerical value for the principal angle in radians.

x≈−0.9273

4. Find the second set of solutions by subtracting the principal value from π

x=π−(−0.9273)≈4.0689

5. Express the complete solution set by adding multiples of the period 2*π

x=arcsin(−4/5)+2*n*π

x=π−arcsin(−4/5)+2*n*π

Final Answer

sin(x)=−4/5⇒x=(−1)n*arcsin(−4/5)+n*π

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