To find the zeros of the function g(x) on the interval 0≤x≤π, we first need to set g(x) equal to zero and solve for x.

The function g(x) is given by g(x) = f(x) + 0.5. Substituting f(x) = sin(2.25x + 0.2) into the equation gives us g(x) = sin(2.25x + 0.2) + 0.5.

Setting g(x) equal to zero gives us the equation sin(2.25x + 0.2) + 0.5 = 0.

To solve for x, we first subtract 0.5 from both sides to isolate the sine function: sin(2.25x + 0.2) = -0.5.

Next, we take the inverse sine (also known as arcsin or sin^-1) of both sides to solve for the angle: 2.25x + 0.2 = arcsin(-0.5).

Subtract 0.2 from both sides: 2.25x = arcsin(-0.5) - 0.2.

Finally, divide both sides by 2.25 to solve for x: x = (arcsin(-0.5) - 0.2) / 2.25.

This gives us the values of x for which g(x) = 0. However, we need to check that these values are within the given interval 0≤x≤π.

Note: The arcsin function returns values in the interval -π/2 ≤ x ≤ π/2. Therefore, if the result is not in the interval 0≤x≤π, we need to add or subtract π to get the result in the correct interval.

Also, keep in mind that the sine function has a period of 2π, so if x is a solution, then x + 2πn is also a solution for any integer n.

This is a numerical problem and it might be easier to solve it using a calculator or a software like MATLAB or Python.

Question

To find the zeros of the function g(x) on the interval 0≤x≤π, we first need to set g(x) equal to zero and solve for x.

The function g(x) is given by g(x) = f(x) + 0.5. Substituting f(x) = sin(2.25x + 0.2) into the equation gives us g(x) = sin(2.25x + 0.2) + 0.5.

Setting g(x) equal to zero gives us the equation sin(2.25x + 0.2) + 0.5 = 0.

To solve for x, we first subtract 0.5 from both sides to isolate the sine function: sin(2.25x + 0.2) = -0.5.

Next, we take the inverse sine (also known as arcsin or sin^-1) of both sides to solve for the angle: 2.25x + 0.2 = arcsin(-0.5).

Subtract 0.2 from both sides: 2.25x = arcsin(-0.5) - 0.2.

Finally, divide both sides by 2.25 to solve for x: x = (arcsin(-0.5) - 0.2) / 2.25.

This gives us the values of x for which g(x) = 0. However, we need to check that these values are within the given interval 0≤x≤π.

Note: The arcsin function returns values in the interval -π/2 ≤ x ≤ π/2. Therefore, if the result is not in the interval 0≤x≤π, we need to add or subtract π to get the result in the correct interval.

Also, keep in mind that the sine function has a period of 2π, so if x is a solution, then x + 2πn is also a solution for any integer n.

This is a numerical problem and it might be easier to solve it using a calculator or a software like MATLAB or Python.

Knowee AI · Accepted Answer