Solve for x sin(x)=15/17

Problem

sin(x)=15/17

Solution

1. Identify the equation as a basic trigonometric equation where you need to find the angle x whose sine is 15/17

2. Apply the inverse sine function to both sides of the equation to isolate x

x=arcsin(15/17)

3. Determine the general solution by considering the periodicity of the sine function and the identity sin(π−θ)=sin(θ)

x=arcsin(15/17)+2*π*n

x=π−arcsin(15/17)+2*π*n

4. Calculate the approximate value using a calculator if a decimal representation is required.

arcsin(15/17)≈1.0808* radians

arcsin(15/17)≈61.93

Final Answer

x=arcsin(15/17)+2*π*n,π−arcsin(15/17)+2*π*n

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