Solve for x 8sin(x)^2-6=0

Problem

8*sin(x)−6=0

Solution

1. Isolate the squared trigonometric term by adding 6 to both sides and then dividing by 8

8*sin(x)=6

sin(x)=6/8

sin(x)=3/4

2. Take the square root of both sides, remembering to include both the positive and negative roots.

sin(x)=±√(,3/4)

sin(x)=±√(,3)/2

3. Identify the reference angle where the sine function equals √(,3)/2 which is π/3 (or 60.

x=π/3+π*k

x=(2*π)/3+π*k

4. Combine the solutions into a general form where k is any integer.

x=π/3+π*k,(2*π)/3+π*k

Final Answer

x=π/3+π*k,(2*π)/3+π*k

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