Respuesta :
Answer:
x=pi/3 + 2pi*k
x=2pi/3+2pi*k
Step-by-step explanation:
sin(x)=sqrt(3)/2
This happens twice in the first rotation on our unit circle.
It happens in the first quadrant and in the second quadrant. Third and fourth quadrants are negative for sine.
So we are looking for when the y-coordinate on the unit circle is sqrt(3)/2.
This is at pi/3 and 2pi/3.
So we can get all the solutions by adding +2pi*k to both of those. This gives us a full rotation about the circle any number of k times. k is an integer.
So the solutions are
x=pi/3 + 2pi*k
x=2pi/3+2pi*k
An equation is formed of two equal expressions. The solution to the equation sin(x)=√3/2 is (π/3 ± 2πn), (2π/3 ± 2πn), where n is any natural number.
What is an equation?
An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
The solution of sinx=√3/2 are,
sin(x) = √3/2
x = sin⁻¹ √3/2
x = (π/3 ± 2πn), (2π/3 ± 2πn)
Hence, the solution to the equation sin(x)=√3/2 is (π/3 ± 2πn), (2π/3 ± 2πn), where n is any natural number.
Learn more about Equation:
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