Question

Solve the equation in the interval from 1.5π to 4.5π. The answer should be in radians, rounded to the nearest hundredth.

sin(x)=0.65.
a) 2.24π
b) 2.60π
c) 3.32π
d) 3.58π

Answer 1

To solve the equation sin(x) = 0.65 in the interval from 1.5π to 4.5π, we use the inverse sine function to find the angles that satisfy the equation.

Step-by-step explanation:

To solve the equation sin(x) = 0.65 in the interval from 1.5π to 4.5π, we need to find the values of x that satisfy the given equation. In this case, we can use the inverse sine function to find the angles whose sine values are equal to 0.65. The inverse sine of 0.65 is approximately 0.72 radians. Since sine is a periodic function, we need to find additional solutions within the given interval. The solutions can be obtained by adding or subtracting multiples of 2π from the initial solution. Rounding the solutions to the nearest hundredth, we have:

a) 2.24π

b) 2.60π

c) 3.32π

d) 3.58π

Therefore, the correct answer is b) 2.60π.