Solve for x sin(x)cos(x)=( square root of 3)/4

Problem

sin(x)*cos(x)=√(,3)/4

Solution

1. Apply the double angle identity for sine, which states sin(2*x)=2*sin(x)*cos(x) by multiplying both sides of the equation by 2

2*sin(x)*cos(x)=2⋅√(,3)/4

2. Simplify the equation to express the left side as a single trigonometric function.

sin(2*x)=√(,3)/2

3. Find the general solutions for the angle 2*x by identifying where the sine function equals √(,3)/2 on the unit circle.

2*x=π/3+2*k*π

2*x=(2*π)/3+2*k*π

4. Solve for x by dividing all terms in both general solution sets by 2 where k is any integer.

x=π/6+k*π

x=π/3+k*π

Final Answer

sin(x)*cos(x)=√(,3)/4⇒x=π/6+k*π,π/3+k*π

Want more problems? Check here!